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.
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)...
R. Pol (1975)
Colloquium Mathematicae
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W. Szlenk (1968)
Studia Mathematica
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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,...
A. V. Arhangel'skii, J. van Mill (2015)
Bulletin of the Polish Academy of Sciences. Mathematics
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We present an example of a separable metrizable topological group G having the property that no remainder of it is (topologically) homogeneous.
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.
M. Valdivia (1977)
Studia Mathematica
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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.
Przemysław Wojtaszczyk (1971)
Studia Mathematica
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Mohammed Yahdi (1998)
Revista Matemática Complutense
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Let C(X) be the set of all convex and continuous functions on a separable infinite dimensional Banach space X, equipped with the topology of uniform convergence on bounded subsets of X. We show that the subset of all convex Fréchet-differentiable functions on X, and the subset of all (not necessarily equivalent) Fréchet-differentiable norms on X, reduce every coanalytic set, in particular they are not Borel-sets.
Tibor Neubrunn, Jaroslav Smítal, Tibor Šalát (1967)
Časopis pro pěstování matematiky
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S. A. Argyros, P. Dodos, V. Kanellopoulos
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