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 -