TY - JOUR

T1 - Productivity of paracompactness in the class of the first-countable GO-spaces with certain dense subsets

AU - Szewczak, P.

PY - 2014/3/15

Y1 - 2014/3/15

N2 - Let P be the class of all spaces whose Cartesian product with every paracompact space is paracompact. We prove that if X is a paracompact, first-countable GO-space with σDC dense subset then X∈P if and only if X is σDC. We also prove that if Y is a metric GO-space and X is a GO-space defined on Y then X is metrizable provided X∈P. These results support the validity of the Telgársky's conjecture which says that if X is a paracompact space then X∈P if and only if the first player of the G(DC, X) game introduced by R. Telgársky, see [13,4,5] has a winning strategy.

AB - Let P be the class of all spaces whose Cartesian product with every paracompact space is paracompact. We prove that if X is a paracompact, first-countable GO-space with σDC dense subset then X∈P if and only if X is σDC. We also prove that if Y is a metric GO-space and X is a GO-space defined on Y then X is metrizable provided X∈P. These results support the validity of the Telgársky's conjecture which says that if X is a paracompact space then X∈P if and only if the first player of the G(DC, X) game introduced by R. Telgársky, see [13,4,5] has a winning strategy.

KW - GO-spaces

KW - Paracompactness

KW - Productivity

UR - http://www.scopus.com/inward/record.url?scp=84896710013&partnerID=8YFLogxK

U2 - 10.1016/j.topol.2014.01.008

DO - 10.1016/j.topol.2014.01.008

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AN - SCOPUS:84896710013

SN - 0166-8641

VL - 165

SP - 39

EP - 49

JO - Topology and its Applications

JF - Topology and its Applications

IS - 1

ER -