Two examples of non-separable metrizable spaces
R. Pol (1975)
Colloquium Mathematicae
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R. Pol (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.
W. J. Davis (1973-1974)
Séminaire Analyse fonctionnelle (dit "Maurey-Schwartz")
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Reinhard Nehse (1981)
Commentationes Mathematicae Universitatis Carolinae
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A. Pełczyński (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,...
Tibor Neubrunn, Jaroslav Smítal, Tibor Šalát (1967)
Časopis pro pěstování matematiky
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M. Valdivia (1977)
Studia Mathematica
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