Displaying similar documents to “Reflexive families of closed sets”

A New Hereditarily l^2 Banach Space

Petsoulas, Giorgos (2009)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: 46B20, 46B26. We construct a non-reflexive, l^2 saturated Banach space such that every non-reflexive subspace has non-separable dual.

Basic Operations on Preordered Coherent Spaces

Klaus Grue, Artur Korniłowicz (2007)

Formalized Mathematics

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This Mizar paper presents the definition of a "Preordered Coherent Space" (PCS). Furthermore, the paper defines a number of operations on PCS's and states and proves a number of elementary lemmas about these operations. PCS's have many useful properties which could qualify them for mathematical study in their own right. PCS's were invented, however, to construct Scott domains, to solve domain equations, and to construct models of various versions of lambda calculus.For more on PCS's,...

Uncountable sets of unit vectors that are separated by more than 1

Tomasz Kania, Tomasz Kochanek (2016)

Studia Mathematica

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Let X be a Banach space. We study the circumstances under which there exists an uncountable set 𝓐 ⊂ X of unit vectors such that ||x-y|| > 1 for any distinct x,y ∈ 𝓐. We prove that such a set exists if X is quasi-reflexive and non-separable; if X is additionally super-reflexive then one can have ||x-y|| ≥ slant 1 + ε for some ε > 0 that depends only on X. If K is a non-metrisable compact, Hausdorff space, then the unit sphere of X = C(K) also contains such a subset; if moreover...

Strong reflexivity of Abelian groups

Montserrat Bruguera, María Jesús Chasco (2001)

Czechoslovak Mathematical Journal

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A reflexive topological group G is called strongly reflexive if each closed subgroup and each Hausdorff quotient of the group G and of its dual group is reflexive. In this paper we establish an adequate concept of strong reflexivity for convergence groups. We prove that complete metrizable nuclear groups and products of countably many locally compact topological groups are BB-strongly reflexive.

Some strongly bounded classes of Banach spaces

Pandelis Dodos, Valentin Ferenczi (2007)

Fundamenta Mathematicae

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We show that the classes of separable reflexive Banach spaces and of spaces with separable dual are strongly bounded. This gives a new proof of a recent result of E. Odell and Th. Schlumprecht, asserting that there exists a separable reflexive Banach space containing isomorphic copies of every separable uniformly convex Banach space.