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Supremum and Infimum - Florida State University - Department ...

Supremum and Infimum Characterizations of Sup and of Inf. Mika Seppälä: Sup and Inf Distance in the Set of Real Numbers The of a number is defined by setting if 0 a

http://www.math.fsu.edu/~seppala/Calculus-2004/HowTo/Supremum/sup.pdf

Date added: August 28, 2013 - Views: 12

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Supremum and Infimum - Florida State University - Department ...

1 Supremum and Infimum Mika Seppälä Mika Seppälä: Sup and Inf Distance in the Set of Real Numbers The of a number is defined by setting

http://www.math.fsu.edu/~seppala/Calculus-2004/HowTo/sup%20and%20inf%20OBSOLETE/ho-sup.pdf

Date added: July 18, 2013 - Views: 9

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Supremum and Infimum

Supremum and Infimum Characterizations of Sup and of Inf. Mika Seppälä: Sup and Inf Index FAQ Distance in the Set of Real Numbers The of a number is defined by setting if 0 a

http://www.webalt.net/Calculus-2004/HowTo/Supremum/sup.pdf

Date added: December 19, 2013 - Views: 4

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The Infimum, Supremum, and Geodesic Length of a Braid ...

The Infimum, Supremum, and Geodesic Length of a Braid Conjugacy Class JoanS.Birman1 1 PartiallysupportedbyNSFGrantsDMS-9705019andDMS-9973232. DepartmentofMathematics,ColumbiaUniversity,NewYork,NewYork10027 E-mail:[email protected] and

http://www.math.columbia.edu/~jb/inf-sup-j.pdf

Date added: April 4, 2012 - Views: 4

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Invexity of supremum and infimum functions

BULL. AUSTRAL. MATH SOC 26A51. 90C30 , VOL. 65 (2002) [289-306] INVEXITY OF SUPREMUM AND INFIMUM FUNCTIONS NGUYEN XUAN HA AND DO VAN LUU Under suitable assumptions we establis theh formulas for calculating generalised

http://journals.cambridge.org/download.php?file=%2FBAZ%2FBAZ65_02%2FS0004972700020335a.pdf&code=bc49ba401b52de6eead73b8e039e5e6c

Date added: August 27, 2014 - Views: 1

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Solved Problems on Supremum and Infimum

Solved Problems on Supremum and Infimum () () + +− + == +− + … 2 2 1 11 Let 1,2,3, . 12 Determine sup and inf .

http://www.webalt.net/Calculus-2004/SolvedProblems/Sup/SupProblems.pdf

Date added: November 24, 2012 - Views: 4

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Infimum and supremum completeness properties of ordered sets ...

Infimum and supremum completeness properties 33 Proof. By the corresponding definitions and Theorem 1.1, it is clear that inf (∅)=max lb(∅) =max(X)=X ∩ ub(X)=ub(X).

http://www.anstuocmath.ro/mathematics/pdf16/BOROS-SZAS-Comp1c.pdf

Date added: July 1, 2012 - Views: 3

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1 Supremum and Infimum 2 Sequences, accumulation points ...

Some fact about sup, inf, limsup and liminf 1 Supremum and Infimum For a set X of real numbers, the number ξ = supX, the supremum of X ( or least upper

http://www.math.umass.edu/~lr7q/ps_files/teaching/math623/sup1.pdf

Date added: January 29, 2012 - Views: 14

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Max, Min, Sup, Inf - Purdue University

The supremum, if it exists, (“sup”, “LUB,” “least upper bound”) of S is the smallest 81. 82 6. MAX, MIN, SUP, INF upper bound for S. An upper bound which actually belongs to the set is called a maximum. Proving that a certain number M is the LUB of a set S is often

http://www.math.purdue.edu/academic/files/courses/2007fall/MA301/MA301Ch6.pdf

Date added: March 12, 2012 - Views: 8

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Given a set, to compute the supremum and infimum of the set,

Given a set, to compute the supremum and infimum of the set, (Step 1) Find out the upper bound and lower bound (if any) of the set (Step 2) Show they are the desired supremum and infimum by applying the theorems

http://www.math.ust.hk/faculty/makyli/202_2007-8FaSp/TNt_07.pdf

Date added: July 18, 2013 - Views: 4

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N p () A p () B - University of Arkansas at Little Rock

They are supremum and infimum of the crude moments and the same bounds of the central moments. These characteristics are determined on the base of the expectation of the function φ(/)X g: M[siφ(/)]supφ(/ ) (/ )d, M[φ(/)]infφ(/ ) (/ )d,

http://ualr.edu/jdberleant/intprob/16.pdf

Date added: August 29, 2013 - Views: 1

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1.3 The Completeness Axiom and some Consequences ...

B. The Supremum and Infimum 1. Definition 1. A nonempty set is bounded above if there exists such that for all , . In this case is said to be

http://math.gmu.edu/~dwalnut/teach/Math315/Summer10/Sec%201.3.pdf

Date added: January 27, 2013 - Views: 5

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Infimum and Supremum of the Set of Real Numbers. Measure Theory

INFIMUM AND SUPREMUM OF THE SET OF REAL. . . 2 (Def. 4) I1 =−∞. One can verify that there exists a set which is negative infinite number-like.

http://www.mizar.org/JFM/pdf/supinf_1.pdf

Date added: August 28, 2013 - Views: 1

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Introduction to Real Analysis - Rowan University

Introduction to Real Analysis . Dr. Marcus Wright . [email protected] Robinson 229D (to the left of the 120-cell, or 4-dim. dodecahedron, as you enter the ... 2.5 Supremum and infimum 2.5.1 A bounded set has a unique least upper bound . 2.6 The Bolzno- Weierstrass Theorem .

http://www.rowan.edu/colleges/las/departments/math/facultystaff/wright/Introduction%20to%20Real%20Analysis%20SPRING%202011.pdf

Date added: October 18, 2012 - Views: 12

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complete lattice/5 where the supremum V and infinum A of a ...

complete lattice/5 where the supremum V and infinum A of a subset $ of P are given by = The partially ordered set P can be embedded into its MacNeille completion • and this embedding is both supremum and infimum dense. That is to say

http://www.math.nmsu.edu/~jharding/1993%20Any%20Lattice%20can%20be%20Reg%20Embedded%20into%20MacNeille%20Comp%20of%20Distrib.pdf

Date added: December 19, 2013 - Views: 2

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Supremum and infimum in Example - KU

Supremum and infimum in [−∞,∞] Axiom + Observation: For all sets A ⊂ [−∞,∞] there is a smallest number larger than all numbers in A called supA – the supremum of A.

http://www.math.ku.dk/~richard/download/courses/Sand1MI_2008/week37monPrint.pdf

Date added: July 18, 2013 - Views: 7

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2.3 Bounds of sets of real numbers - Ohio State University

2.3 Bounds of sets of real numbers 2.3.1 Upper bounds of a set; the least upper bound (supremum) Consider S a set of real numbers. S is called bounded above if there is a number M so that any x ∈ S is

http://math.osu.edu/~costin.10/H161/supremum%20copy.pdf

Date added: January 21, 2014 - Views: 3

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Infimum and Supremum of the Set of Real Numbers. Measure Theory

Infimum and Supremum of the Set of Real ... 167 Let X be a non-empty subset of . The functor X yields a non-empty subset of and is defined by:

http://fm.mizar.org/1991-2/pdf2-1/supinf_1.pdf

Date added: August 29, 2013 - Views: 2

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Real numbers - Department of Mathematics, University of Toronto

Supremum and infimum Limits and real numbers Page 5. Definition. A sequence of real numbers is called ... Every bounded bellow decreasing sequence converges to its infimum. Proof. Enough to prove for increasing sequences. Let Then . Since is increasing, .

http://www.math.toronto.edu/ilia/Teaching/MAT378.2010/Limits%20and%20real%20numbers.pdf

Date added: October 17, 2011 - Views: 6

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The Supremum of Some Canonical Processes

The Supremum of Some Canonical Processes Author(s): Michel Talagrand Source: American Journal of Mathematics, Vol. 116, No. 2 (Apr., 1994), pp. 283-325 ... where the infimum is taken over all the increasing sequences of partitions of T,

http://students.mimuw.edu.pl/~tt249057/other/ksiazki%20i%20papery/talagrand-supremum%20of%20some%20canonical%20processes.pdf

Date added: January 8, 2014 - Views: 4

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COMPLETE LATTICES - San Francisco State University

complete lattice. For example, consider < PS,f> for any set S, < I,#> for any bounded interval I of natural numbers, ... subset of X has an infimum, for the supremum of a set is then the infimum of the set of all its upper bounds. Dually, ...

http://math.sfsu.edu/smith/Math800/Units/CompleteLattices.pdf

Date added: July 18, 2013 - Views: 3

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Chapter2

Chapter2 The supremum and infimum We review the definition of the supremum and and infimum and some of their properties that we use in defining and analyzing the Riemann integral.

http://www.math.ucdavis.edu/~hunter/m125b/ch2.pdf

Date added: June 2, 2013 - Views: 1

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Metric spaces - Department of Mathematics, University of Toronto

A metric space is called complete if every Cauchy sequence converges to a limit. Already know: ... By the definition of supremum and infimum, for any we have Let be a continuous function. Then is bounded (i.e. is a bounded set). Moreover, it ...

http://www.math.toronto.edu/ilia/Teaching/MAT378.2010/Metric%20Spaces.pdf

Date added: October 31, 2011 - Views: 7

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2.4 The Completeness Property of R - Kennesaw State University

The completeness property is also known as the least upper bound property. ... Supremum and In–mum of a Set De–nition 143 (Supremum and in–mum) Let Sbe a subset of R 1. If Sis bounded above, then an upper bound of Sis said to be a supremum

http://math.kennesaw.edu/~plaval/math4381/lubprop.pdf

Date added: July 16, 2014 - Views: 1

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Gap functions for generalized vector equilibrium problems via ...

supremum/infimum of a set, defined in terms of a closure of the set, three kinds of conjugate dual problems are investigated by considering the different perturbations to GVEP. Then, gap functions for GVEP are established by using the weak and strong duality results.

http://www.tandfonline.com/doi/pdf/10.1080/00036811.2012.724403

Date added: August 27, 2014 - Views: 1

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EKSISTENSI SUPREMUM DAN INFIMUM DENGAN TEOREMA CANTOR ...

EKSISTENSI SUPREMUM DAN INFIMUM DENGAN TEOREMA CANTOR DEDEKIND Nursiya Bito Staf Dosen Jurusan Matematika dan IPA Universitas Negeri Gorontalo ABSTRACT: In this paper, we will try to proof existence of supremum and infimum with Cantor

http://ejurnal.ung.ac.id/index.php/ST/article/download/369/361

Date added: January 21, 2014 - Views: 1

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UNIFORM APPROXIMATION BY CLASSES OF FUNCTIONS CLOSED UNDER ...

closed under pointwise supremum and infimum, respectively. Concerning the interpretation - of the functional hulls 7 and 1, a favorable case is when t,he classes Iio and Lo can be easily identified as, for example, bvhen Iio is the class of continuous functions on a - metric ...

http://www.tandfonline.com/doi/pdf/10.1080/01630569108816413

Date added: June 27, 2014 - Views: 2

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Section B Properties of Upper and Lower Bounds

Chapter 5 Real Numbers 12 Section B Properties of Upper and Lower Bounds By the end of this section you will be able to • prove properties of the supremum and infimum of a set

http://mathsforall.co.uk/userfiles/5B%20Properties%20of%20Upper%20and%20Lower%20Bounds.pdf

Date added: October 19, 2012 - Views: 5

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Fast infimum-supremum interval operations for double-double ...

Fast infimum-supremum interval operations for double-double arithmetic in rounding-to-nearest Naoya Yamanaka (Waseda University) Shin’ichi Oishi

http://conf.nsc.ru/files/conferences/scan2012/141503/Yamanaka-scan2012.pdf

Date added: January 21, 2014 - Views: 2

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Southern University and A&M College - Department of ...

theorems: Axioms of the real numbers, supremum, infimum, upper limits, open and closed sets in n R, compactness, the Bolzano-Weierstrass and Heine-Borel ... www.math.subr.edu/faculty/javier.html IV. Instructional Procedures

http://www.math.subr.edu/syllabus/Math%20565%20Javier.pdf

Date added: July 18, 2013 - Views: 2

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SYLLABUS FOR ENTRANCE EXAMINATION FOR M - Maths Panache

system as a complete ordered field, Archimedean property, supremum, infimum. Sequence and series, Convergence, limsup, liminf. Bolzano Weierstrass theorem, Heine Borel theorem. Continuity, Uniform continuity, Intermediate value theorem, Differentiability, Mean value ...

http://www.mathspanache.com/PDF/du_Syllabus.pdf

Date added: July 28, 2014 - Views: 1

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The Law of the Supremum of a Stable Lévy Process with No ...

THE LAW OF THE SUPREMUM OF A STABLE LEVY PROCESS 1779 and no series representation for the density function of St seems to be available in

http://www.jstor.org/stable/25450628

Date added: July 31, 2013 - Views: 1

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Southern University and A&M College - Department of ...

SOUTHERN UNIVERSITY AND A&M COLLEGE Baton Rouge, Louisiana DEPARTMENT OF MATHEMATICS COURSE SYLLABUS Real Analysis I. Descriptive Information ... numbers by finding supremum and infimum of sets and using the completeness property of real numbers.

http://www.math.subr.edu/syllabus/MATH%20462%20REAL%20ANALYSIS%20(U).pdf

Date added: June 18, 2012 - Views: 5

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THE LOCAL SUPREMUM PRINCIPLE FOR OPTIMUM CONTROL PROBLEMS ...

THE LOCAL SUPREMUM PRINCIPLE FOR OPTIMUM CONTROL PROBLEMS WITH NONSCALAR-VALUED PERFORMANCE CRITERION By ... (infimum) in form of the local supremum principle for optimum control problems with nonscalar-valued performance criterion.

http://www.pp.bme.hu/ee/article/download/4924/4029

Date added: June 27, 2014 - Views: 1

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The Riemann Integral

upper integral of 𝑓 (on the interval [𝑎, 𝑏]) is the infimum of 𝑈(𝑓, 𝑃), taken over all partitions 𝑃. Likewise, 𝐿(𝑓), the lower integral of 𝑓 (on the interval [𝑎, 𝑏]) is the supremum of 𝐿(𝑓, 𝑃), taken over all partitions 𝑃.

http://math.la.asu.edu/~boerner/bridge/The%20Riemann%20Integral.pdf

Date added: February 20, 2014 - Views: 1

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Yi Shen Title: Stationarity and Random Locations

locations including, for example, the location of the path supremum/infimum over an interval, the first/last hitting time, among many others. On one hand, it is proved that under stationarity, the

http://www.orie.cornell.edu/orie/upload/Yi-Shen-abstract.pdf

Date added: January 21, 2014 - Views: 1

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Suprema/In ma Review Sheet - Michigan State University

to have a supremum or in mum in the event that it is not bounded, or is empty. We will extend the de nitions of sup and inf to these cases by using the following conventions: (1)If A is not bounded above, we de ne supA = +1.

http://math.msu.edu/~siefring/mth421_s10/sup_inf.pdf

Date added: October 13, 2013 - Views: 4

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AN ¿'-SPACE FOR BOOLEAN ALGEBRAS AND SEMIREFLEXIVITY OF ...

the definition of bounded subset, supremum and infimum are evident. & is called complete if every subset of & has a supremum in 3. and o-complete if Presented to the Society, March 4, 1976 under the title Boolean algebras and L and £°° spaces;

http://www.ams.org/journals/tran/1977-226-00/S0002-9947-1977-0430769-3/S0002-9947-1977-0430769-3.pdf

Date added: August 29, 2013 - Views: 2

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∈𝐍

Find the infimum and supremum of the set S = 1 + 2 n: n ∈𝐍 ∪ 4 −2q q: q ∈𝐐∩(1, ∞)) (Step 1) IDEA: We first find out the upper bound and lower bound of each set and combine them . Upper Bound Lower Bound A = 1 + 2 n: n ∈𝐍

http://www.math.ust.hk/~makyli/202_2007-8FaSp/TNt_08.pdf

Date added: January 21, 2014 - Views: 1

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log w(o s[s d(] d

THE SUPREMUM AND INFIMUM OF THE POISSON PROCESS' BY RONALD PYKE Columbia University 1. Introduction. Let {X(t); t ? 0} be a separable Poisson process with shift

http://www.jstor.org/stable/2237099

Date added: August 27, 2014 - Views: 1

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Jaworski, B. (Ed.) Proceedings of the British Society for ...

THE CONCEPT OF SUPREMUM/INFIMUM OF A SET: A PROBLEMATIC OVERTURE TO THE CONCEPT OF LIMIT? Elena Nardi School of Education, University of East Anglia

http://www.bsrlm.org.uk/IPs/ip20-12/BSRLM-IP-20-12-20.pdf

Date added: August 27, 2014 - Views: 1

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Common Fixed Points of Increasing Operators in Posets and ...

2126 M. L. Diviccaro and S. Sessa semilattice) if any nonempty subset of S has supremum (resp. infimum) in S. S is

http://www.m-hikari.com/imf-password2008/41-44-2008/sessaIMF41-44-2008.pdf

Date added: May 30, 2013 - Views: 3

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Definitions and Propositions

supremum sup{x,y} and the infimum inf{x,y}. Definition A.10 - Complete Lattice A lattice A = (A, ≤) is called complete, if and only if any arbitrary subset X ⊆ A contains a supremum and an infimum. Remark A.11 According to Definition A.10 - Complete ...

http://www.algebraworkbench.net/en/documentation/theory/theory1b_en.pdf

Date added: August 27, 2014 - Views: 1

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Involuntary Unemployment as a Perfect Equilibrium in a ...

INVOLUNTARY UNEMPLOYMENT AS A PERFECT EQUILIBRIUM IN A BARGAINING MODEL BY ... have a unique solution. Thus the infimum, and the supremum, of the firm's payoff in any Perfect Equilibrium partition, coincide. It is straightforward to show that this solution is indeed supported by a pair

http://www.jstor.org/stable/1913509

Date added: January 21, 2014 - Views: 1

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4 Supremum, Infimum - IAG - Institut für Algebraische Geometrie

4 Supremum, Infimum 18 Wir sehen an diesem Beispiel, dass im allgemeinen eine nicht leere, nach oben beschr¨ankte Menge kein Supremum zu haben braucht.

http://www.iag.uni-hannover.de/fileadmin/institut/team/hulek/AnalysisA/Kapitel4.pdf

Date added: August 27, 2014 - Views: 1

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Problems and Comments on Relations Chapter 8

Problems and Comments on Relations Chapter 8 Section 8.1, Problems: 1, 24, 30, 47, 53 Section 8.4, Problems: 1, 2, 3, 22, 23 ... least upper bound is called the supremum of S. Infimum is similarly defined as the largest lower bound of a set S. The open interval 0,1 of real numbers has infimum 0

http://www.math.uh.edu/~klaus/discrete_math_chapter_7.pdf

Date added: January 14, 2013 - Views: 3

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Problems and Comments on Relations Chapter 9

subset S has a supremum and an infimum. For any set S the powerset P S with inclusion as partial ordering is an example of a complete lattice. The infimum of a set of subsets is its intersection, the supremum is its union. A partially ordered set L,

http://www.math.uh.edu/~klaus/2012SU_5336_9.pdf

Date added: October 12, 2013 - Views: 4

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MATHEMATICS - Gyan Vihar

MATHEMATICS UNIT – I Elementary set theory, finite, countable and uncountable sets, Real number system, supremum, infimum, Sequences and series, convergence, limsup, liminf, Bolzano Weierstrass theorem,

http://gyanvihar.org/MATHEMATICS.pdf

Date added: May 12, 2013 - Views: 3

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Convergence properties of generalized Benders decompositions

consists of those values of y for which (3) is feasible; YnV is the projection of the feasible region of (1) onto the y-space. The following theorem (Geoffrion, 1970) ... minimize [ supremum { infimum [ /(x, y) + uT G(x, y) s.t. (5) ] } ] (8)

http://repository.cmu.edu/cgi/viewcontent.cgi?article=1170&context=cheme

Date added: March 13, 2014 - Views: 1

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SPECTRAL-LIKE DUALITY FOR DISTRIBUTIVE HILBERT ALGEBRAS WITH ...

SPECTRAL-LIKE DUALITY FOR DISTRIBUTIVE HILBERT ALGEBRAS WITH INFIMUM SERGIO A. CELANI AND MAR IA ESTEBAN Abstract. Distributive Hilbert Algebras with in mum, or DH^-algebras, are

http://www.ub.edu/grlnc/docs/Hilbert-Infimo.pdf

Date added: August 27, 2014 - Views: 1