A sequential property of CP(X) and a covering property of hurewicz

Marion Scheepers

doi:10.1090/s0002-9939-97-03897-5

A sequential property of C_P(X) and a covering property of hurewicz

Marion Scheepers

Mathematics Department

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

23 Scopus citations

Abstract

C_P(X) has the monotonie sequence selection property if there is for each /, and for every sequence (σ_n : n < LJ) where for each n σ_n is a sequence converging poiritwise monotonically to /, a sequence (F_n : n < w) such that for each n f_n is a term of σn, and (f_n : n < w) converges pointwise to J. We prove a theorem which implies for metric spaces X that C_P(X) has the monotonie sequence selection property if, and only if, X has a covering property of Hurewicz.

Original language	English
Pages (from-to)	2789-2795
Number of pages	7
Journal	Proceedings of the American Mathematical Society
Volume	125
Issue number	9
DOIs	https://doi.org/10.1090/s0002-9939-97-03897-5
State	Published - 1997

Keywords

Countable fan tightness
Countable strong fan tightness
Cov(a1),∂,p
Hurewicz property
Lusin set, menger property
Rothberger property
Si(Γ,Γ),b
Sierpiriski set
Strong fréchet property
γ-set

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title = "A sequential property of CP(X) and a covering property of hurewicz",

abstract = "CP(X) has the monotonie sequence selection property if there is for each /, and for every sequence (σn : n < LJ) where for each n σn is a sequence converging poiritwise monotonically to /, a sequence (Fn : n < w) such that for each n fn is a term of σn, and (fn : n < w) converges pointwise to J. We prove a theorem which implies for metric spaces X that CP(X) has the monotonie sequence selection property if, and only if, X has a covering property of Hurewicz.",

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AB - CP(X) has the monotonie sequence selection property if there is for each /, and for every sequence (σn : n < LJ) where for each n σn is a sequence converging poiritwise monotonically to /, a sequence (Fn : n < w) such that for each n fn is a term of σn, and (fn : n < w) converges pointwise to J. We prove a theorem which implies for metric spaces X that CP(X) has the monotonie sequence selection property if, and only if, X has a covering property of Hurewicz.

KW - Countable fan tightness

KW - Countable strong fan tightness

KW - Cov(a1),∂,p

KW - Hurewicz property

KW - Lusin set, menger property

KW - Rothberger property

KW - Si(Γ,Γ),b

KW - Sierpiriski set

KW - Strong fréchet property

KW - γ-set

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JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 9

ER -

A sequential property of C_P(X) and a covering property of hurewicz

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Keywords

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