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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A. T. Charlesworth, R. E. Hodel, F. D. Tall (1975)
Colloquium Mathematicae
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Robert Moore (1926)
Fundamenta Mathematicae
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The purpose of this paper is to establish two theorems: Theoreme: In order that every subclass of a given class D of Fréchet should be separable it is necessary and sufficient that every uncountable subclass of that class D should have a limit point. Theoreme: If D_s is a separable class D then every uncountable subclass of D_s contains a point of condensation.
Tibor Neubrunn, Jaroslav Smítal, Tibor Šalát (1967)
Časopis pro pěstování matematiky
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Elżbieta Pol (1978)
Colloquium Mathematicae
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K. Alster (1982)
Colloquium Mathematicae
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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,...
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)...
M. Valdivia (1977)
Studia Mathematica
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David Bryant, André Nies, Paul Tupper (2017)
Analysis and Geometry in Metric Spaces
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The Urysohn space is a separable complete metric space with two fundamental properties: (a) universality: every separable metric space can be isometrically embedded in it; (b) ultrahomogeneity: every finite isometry between two finite subspaces can be extended to an auto-isometry of the whole space. The Urysohn space is uniquely determined up to isometry within separable metric spaces by these two properties. We introduce an analogue of the Urysohn space for diversities, a recently developed...
G. Reed (1976)
Fundamenta Mathematicae
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G.A. Elliott, K. Thomsen (1994)
Geometric and functional analysis
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Eric van Douwen, Teodor Przymusiński (1980)
Fundamenta Mathematicae
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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.