TY - JOUR

T1 - Productivity of paracompactness in the class of GO-spaces

AU - Alster, K.

AU - Szewczak, P.

PY - 2013/11/1

Y1 - 2013/11/1

N2 - 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.

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.

KW - GO-spaces

KW - Paracompactness

KW - Productivity

UR - http://www.scopus.com/inward/record.url?scp=84885841873&partnerID=8YFLogxK

U2 - 10.1016/j.topol.2013.09.002

DO - 10.1016/j.topol.2013.09.002

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AN - SCOPUS:84885841873

SN - 0166-8641

VL - 160

SP - 2183

EP - 2195

JO - Topology and its Applications

JF - Topology and its Applications

IS - 17

ER -