Cp(X) and Arhangel'skiǐ's αi-spaces

Marion Scheepers

doi:10.1016/s0166-8641(97)00218-6

C_p(X) and Arhangel'skiǐ's α_i-spaces

Marion Scheepers

Mathematics Department

Research output: Contribution to journal › Article › peer-review

32 Scopus citations

Abstract

Nogura showed that whereas Arhangel'skiǐ's properties α₁, α₂ and α₃ are preserved by finite products, the property α₄ is not. It is shown here that for each space X the properties α₂, α₃ and α₄, are the same for the function space C_p(X). As a consequence, α₄ is closed under finite products of such function spaces.

Original language	English
Pages (from-to)	265-275
Number of pages	11
Journal	Topology and its Applications
Volume	89
Issue number	3
DOIs	https://doi.org/10.1016/s0166-8641(97)00218-6
State	Published - 1998

Keywords

C(X)
QN-space
S(Γ, Γ)
Sierpiński set
α-space

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10.1016/s0166-8641(97)00218-6

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@article{33c0d2a11ad64fd1a9ac767af1de3ff3,

title = "Cp(X) and Arhangel'skiǐ's αi-spaces",

abstract = "Nogura showed that whereas Arhangel'skiǐ's properties α1, α2 and α3 are preserved by finite products, the property α4 is not. It is shown here that for each space X the properties α2, α3 and α4, are the same for the function space Cp(X). As a consequence, α4 is closed under finite products of such function spaces.",

keywords = "C(X), QN-space, S(Γ, Γ), Sierpi{\'n}ski set, α-space",

author = "Marion Scheepers",

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T1 - Cp(X) and Arhangel'skiǐ's αi-spaces

AU - Scheepers, Marion

PY - 1998

Y1 - 1998

N2 - Nogura showed that whereas Arhangel'skiǐ's properties α1, α2 and α3 are preserved by finite products, the property α4 is not. It is shown here that for each space X the properties α2, α3 and α4, are the same for the function space Cp(X). As a consequence, α4 is closed under finite products of such function spaces.

AB - Nogura showed that whereas Arhangel'skiǐ's properties α1, α2 and α3 are preserved by finite products, the property α4 is not. It is shown here that for each space X the properties α2, α3 and α4, are the same for the function space Cp(X). As a consequence, α4 is closed under finite products of such function spaces.

KW - C(X)

KW - QN-space

KW - S(Γ, Γ)

KW - Sierpiński set

KW - α-space

UR - http://www.scopus.com/inward/record.url?scp=15944423301&partnerID=8YFLogxK

U2 - 10.1016/s0166-8641(97)00218-6

DO - 10.1016/s0166-8641(97)00218-6

M3 - Article

AN - SCOPUS:15944423301

SN - 0016-660X

VL - 89

SP - 265

EP - 275

JO - Topology and its Applications

JF - Topology and its Applications

IS - 3

ER -

C_p(X) and Arhangel'skiǐ's α_i-spaces

Abstract

Keywords

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