On a theorem of Jones and Heath concerning separable normal spaces
A. T. Charlesworth, R. E. Hodel, F. D. Tall (1975)
Colloquium Mathematicae
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Displaying similar documents to “Concerning the relation between separability and the proposition that every uncountable point set has a limit point”
On a theorem of Jones and Heath concerning separable normal spaces
Separable reduction theorems by the method of elementary submodels
Marek Cúth (2012)
Fundamenta Mathematicae
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We simplify the presentation of the method of elementary submodels and we show that it can be used to simplify proofs of existing separable reduction theorems and to obtain new ones. Given a nonseparable Banach space X and either a subset A ⊂ X or a function f defined on X, we are able for certain properties to produce a separable subspace of X which determines whether A or f has the property in question. Such results are proved for properties of sets: of being dense, nowhere dense,...
Two examples of non-separable metrizable spaces
R. Pol (1975)
Colloquium Mathematicae
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The controlled separable projection property for Banach spaces
Jesús Ferrer, Marek Wójtowicz (2011)
Open Mathematics
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Let X, Y be two Banach spaces. We say that Y is a quasi-quotient of X if there is a continuous operator R: X → Y such that its range, R(X), is dense in Y. Let X be a nonseparable Banach space, and let U, W be closed subspaces of X and Y, respectively. We prove that if X has the Controlled Separable Projection Property (CSPP) (this is a weaker notion than the WCG property) and Y is a quasi-quotient of X, then the structure of Y resembles the structure of a separable Banach space: (a)...
On certain properties characterizing locally separable metric spaces
Tibor Neubrunn, Jaroslav Smítal, Tibor Šalát (1967)
Časopis pro pěstování matematiky
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A strong boundedness result for separable Rosenthal compacta
Pandelis Dodos (2008)
Fundamenta Mathematicae
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It is proved that the class of separable Rosenthal compacta on the Cantor set having a uniformly bounded dense sequence of continuous functions is strongly bounded.
Separable extensions of first countable spaces
Eric van Douwen, Teodor Przymusiński (1980)
Fundamenta Mathematicae
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On differentiability of strongly α(·)-paraconvex functions in non-separable Asplund spaces
S. Rolewicz (2005)
Studia Mathematica
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In Rolewicz (2002) it was proved that every strongly α(·)-paraconvex function defined on an open convex set in a separable Asplund space is Fréchet differentiable on a residual set. In this paper it is shown that the assumption of separability is not essential.
On class of Banach spaces
M. Valdivia (1977)
Studia Mathematica
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The undecidability of the existence of a non-separable normal Moore space satisfying the countable chain condition
T. Przymusiński, F. Tall (1974)
Fundamenta Mathematicae
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On subspaces of separable first countable -spaces
G. Reed (1976)
Fundamenta Mathematicae
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Some Applications of Simons’ Inequality
Godefroy, Gilles (2000)
Serdica Mathematical Journal
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We survey several applications of Simons’ inequality and state related open problems. We show that if a Banach space X has a strongly sub-differentiable norm, then every bounded weakly closed subset of X is an intersection of finite union of balls.
Sequences of 0's and 1's: sequence spaces with the separable Hahn property
Maria Zeltser (2007)
Studia Mathematica
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In [3] it was discovered that one of the main results in [1] (Theorem 5.2), applied to three spaces, contains a nontrivial gap in the argument, but neither the gap was closed nor a counterexample was provided. In [4] the authors verified that all three above mentioned applications of the theorem are true and stated a problem concerning the topological structure of one of these three spaces. In this paper we answer the problem and give a counterexample to the theorem in doubt. Also we...
Sequential + separable vs sequentially separable and another variation on selective separability
Angelo Bella, Maddalena Bonanzinga, Mikhail Matveev (2013)
Open Mathematics
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A space X is sequentially separable if there is a countable D ⊂ X such that every point of X is the limit of a sequence of points from D. Neither “sequential + separable” nor “sequentially separable” implies the other. Some examples of this are presented and some conditions under which one of the two implies the other are discussed. A selective version of sequential separability is also considered.