Please use this identifier to cite or link to this item: http://hdl.handle.net/10995/101529
Title: Topological properties of some function spaces
Authors: Gabriyelyan, S.
Osipov, A. V.
Issue Date: 2020
Publisher: Elsevier B.V.
Citation: Gabriyelyan S. Topological properties of some function spaces / S. Gabriyelyan, A. V. Osipov. — DOI 10.1016/j.topol.2020.107248 // Topology and its Applications. — 2020. — Vol. 279. — 107248.
Abstract: Let Y be a metrizable space containing at least two points, and let X be a YI-Tychonoff space for some ideal I of compact sets of X. Denote by CI(X,Y) the space of continuous functions from X to Y endowed with the I-open topology. We prove that CI(X,Y) is Fréchet–Urysohn iff X has the property γI. We characterize zero-dimensional Tychonoff spaces X for which the space CI(X,2) is sequential. Extending the classical theorems of Gerlits, Nagy and Pytkeev we show that if Y is not compact, then Cp(X,Y) is Fréchet–Urysohn iff it is sequential iff it is a k-space iff X has the property γ. An analogous result is obtained for the space of bounded continuous functions taking values in a metrizable locally convex space. Denote by B1(X,Y) and B(X,Y) the space of Baire one functions and the space of all Baire functions from X to Y, respectively. If H is a subspace of B(X,Y) containing B1(X,Y), then H is metrizable iff it is a σ-space iff it has countable cs⁎-character iff X is countable. If additionally Y is not compact, then H is Fréchet–Urysohn iff it is sequential iff it is a k-space iff it has countable tightness iff Xℵ0 has the property γ, where Xℵ0 is the space X with the Baire topology. We show that if X is a Polish space, then the space B1(X,R) is normal iff X is countable. © 2020 Elsevier B.V.
Keywords: BAIRE FUNCTION
CP(X,Y)
CS⁎-CHARACTER
FRÉCHET–URYSOHN
FUNCTION SPACE
IDEAL OF COMPACT SETS
K-SPACE
METRIC SPACE
NORMAL
SEQUENTIAL
Σ-SPACE
URI: http://hdl.handle.net/10995/101529
Access: info:eu-repo/semantics/openAccess
SCOPUS ID: 85084351854
PURE ID: 12905129
632ed029-7655-4d45-82f0-c17a1e5a621a
ISSN: 1668641
DOI: 10.1016/j.topol.2020.107248
Appears in Collections:Научные публикации, проиндексированные в SCOPUS и WoS CC

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