Please use this identifier to cite or link to this item: http://hdl.handle.net/10995/101997
Title: Classification of selectors for sequences of dense sets of Cp(X)
Authors: Osipov, A. V.
Issue Date: 2018
Publisher: Elsevier B.V.
Citation: Osipov A. V. Classification of selectors for sequences of dense sets of Cp(X) / A. V. Osipov. — DOI 10.1016/j.topol.2018.04.010 // Topology and its Applications. — 2018. — Vol. 242. — P. 20-32.
Abstract: For a Tychonoff space X, Cp(X) is the space of all real-valued continuous functions with the topology of pointwise convergence. A subset A⊂X is said to be sequentially dense in X if every point of X is the limit of a convergent sequence in A. In this paper, the following 8 properties for Cp(X) are considered. S1(S,S)⇒Sfin(S,S)⇒S1(S,D)⇒Sfin(S,D)⇑⇑⇑⇑S1(D,S)⇒Sfin(D,S)⇒S1(D,D)⇒Sfin(D,D) For example, a space X satisfies S1(D,S) (resp., Sfin(D,S)) if whenever {Dn:n∈N} is a sequence of dense subsets of X, one can take points xn∈Dn (resp., finite Fn⊂Dn) such that {xn:n∈N} (resp., ⋃{Fn:n∈N}) is sequentially dense in X. Other properties are defined similarly. S1(D,D) (=R-separability) and Sfin(D,D) (=M-separability) for Cp(X) were already investigated by several authors. In this paper, we have gave characterizations for Cp(X) to satisfy other 6 properties above. © 2018
Keywords: CP THEORY
FUNCTION SPACES
M-SEPARABILITY
R-SEPARABILITY
S1(D,D)
S1(D,S)
S1(S,D)
S1(S,S)
SFIN(D,D)
SFIN(D,S)
SFIN(S,D)
SFIN(S,S)
SCHEEPERS DIAGRAM
SELECTION PRINCIPLES
URI: http://hdl.handle.net/10995/101997
Access: info:eu-repo/semantics/openAccess
SCOPUS ID: 85046363499
PURE ID: 7276814
5a0c94e0-2a14-4d3c-b925-a41e77960820
ISSN: 1668641
DOI: 10.1016/j.topol.2018.04.010
Appears in Collections:Научные публикации, проиндексированные в SCOPUS и WoS CC

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