Baire spaces and some generalizations of complete metric spaces
Zdeněk Frolík (1961)
Czechoslovak Mathematical Journal
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Zdeněk Frolík (1961)
Czechoslovak Mathematical Journal
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Darji, Udayan B. (1996)
Journal of Applied Analysis
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Zbigniew Piotrowski (1981)
Colloquium Mathematicae
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Choban, Mitrofan (1998)
Serdica Mathematical Journal
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Let a compact Hausdorff space X contain a non-empty perfect subset. If α < β and β is a countable ordinal, then the Banach space Bα (X) of all bounded real-valued functions of Baire class α on X is a proper subspace of the Banach space Bβ (X). In this paper it is shown that: 1. Bα (X) has a representation as C(bα X), where bα X is a compactification of the space P X – the underlying set of X in the Baire topology generated by the Gδ -sets in X. 2. If 1 ≤ α < β ≤ Ω, where...
Jack Brown (1977)
Fundamenta Mathematicae
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Jerzy Kąkol (1986)
Mathematica Slovaca
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Gloria Tashjian (1977)
Fundamenta Mathematicae
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Evgenij G. Pytkeev (1990)
Commentationes Mathematicae Universitatis Carolinae
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Mats Aigner, Vitalij A. Chatyrko, Venuste Nyagahakwa (2013)
Colloquium Mathematicae
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We suggest a method of constructing decompositions of a topological space X having an open subset homeomorphic to the space (ℝⁿ,τ), where n is an integer ≥ 1 and τ is any admissible extension of the Euclidean topology of ℝⁿ (in particular, X can be a finite-dimensional separable metrizable manifold), into a countable family ℱ of sets (dense in X and zero-dimensional in the case of manifolds) such that the union of each non-empty proper subfamily of ℱ does not have the Baire property...