Productivity of paracompactness in the class of GO-spaces

K. Alster; P. Szewczak

doi:10.1016/j.topol.2013.09.002

Productivity of paracompactness in the class of GO-spaces

K. Alster
, P. Szewczak

Cardinal Stefan Wyszynski University

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

4 Scopus citations

Abstract

The main result of the paper says that if X is a paracompact GO-space, meaning a subspace of a linearly ordered space and M a paracompact space satisfying the first axiom of countability such that X can be embedded in M^ω1 then the product X×Y is paracompact for every paracompact space Y if and only if the first player of the G(DC, X) game, introduced by Telgarsky has a winning strategy. In particular we obtain that if X is paracompact GO-space of weight not greater than ω₁ then the product X×Y is paracompact for every paracompact space Y if and only if the first player of the G(DC, X) game has a winning strategy.

Original language	English
Pages (from-to)	2183-2195
Number of pages	13
Journal	Topology and its Applications
Volume	160
Issue number	17
DOIs	https://doi.org/10.1016/j.topol.2013.09.002
State	Published - 1 Nov 2013
Externally published	Yes

Keywords

GO-spaces
Paracompactness
Productivity

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10.1016/j.topol.2013.09.002

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AB - The main result of the paper says that if X is a paracompact GO-space, meaning a subspace of a linearly ordered space and M a paracompact space satisfying the first axiom of countability such that X can be embedded in Mω1 then the product X×Y is paracompact for every paracompact space Y if and only if the first player of the G(DC, X) game, introduced by Telgarsky has a winning strategy. In particular we obtain that if X is paracompact GO-space of weight not greater than ω1 then the product X×Y is paracompact for every paracompact space Y if and only if the first player of the G(DC, X) game has a winning strategy.

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ER -

Productivity of paracompactness in the class of GO-spaces

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Keywords

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