On $\pi$-metrizable spaces, their continuous images and products

Stover, Derrick. "On $\pi $-metrizable spaces, their continuous images and products." Commentationes Mathematicae Universitatis Carolinae 50.1 (2009): 153-162. <http://eudml.org/doc/32489>.

@article{Stover2009,
abstract = {A space $X$ is said to be $\pi $-metrizable if it has a $\sigma $-discrete $\pi $-base. The behavior of $\pi $-metrizable spaces under certain types of mappings is studied. In particular we characterize strongly $d$-separable spaces as those which are the image of a $\pi $-metrizable space under a perfect mapping. Each Tychonoff space can be represented as the image of a $\pi $-metrizable space under an open continuous mapping. A question posed by Arhangel’skii regarding if a $\pi $-metrizable topological group must be metrizable receives a negative answer.},
author = {Stover, Derrick},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {$\pi $-metrizable; weakly $\pi $-metrizable; $\pi $-base; $\sigma $-discrete $\pi $-base; $\sigma $-disjoint $\pi $-base; $d$-separable; -metrizable space; weakly -metrizable space; -base},
language = {eng},
number = {1},
pages = {153-162},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On $\pi $-metrizable spaces, their continuous images and products},
url = {http://eudml.org/doc/32489},
volume = {50},
year = {2009},
}

TY - JOUR
AU - Stover, Derrick
TI - On $\pi $-metrizable spaces, their continuous images and products
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2009
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 50
IS - 1
SP - 153
EP - 162
AB - A space $X$ is said to be $\pi $-metrizable if it has a $\sigma $-discrete $\pi $-base. The behavior of $\pi $-metrizable spaces under certain types of mappings is studied. In particular we characterize strongly $d$-separable spaces as those which are the image of a $\pi $-metrizable space under a perfect mapping. Each Tychonoff space can be represented as the image of a $\pi $-metrizable space under an open continuous mapping. A question posed by Arhangel’skii regarding if a $\pi $-metrizable topological group must be metrizable receives a negative answer.
LA - eng
KW - $\pi $-metrizable; weakly $\pi $-metrizable; $\pi $-base; $\sigma $-discrete $\pi $-base; $\sigma $-disjoint $\pi $-base; $d$-separable; -metrizable space; weakly -metrizable space; -base
UR - http://eudml.org/doc/32489
ER -