On weakly monotonically monolithic spaces

Liang-Xue Peng

Commentationes Mathematicae Universitatis Carolinae (2010)

  • Volume: 51, Issue: 1, page 133-142
  • ISSN: 0010-2628

Abstract

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In this note, we introduce the concept of weakly monotonically monolithic spaces, and show that every weakly monotonically monolithic space is a D -space. Thus most known conclusions on D -spaces can be obtained by this conclusion. As a corollary, we have that if a regular space X is sequential and has a point-countable w c s * -network then X is a D -space.

How to cite

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Peng, Liang-Xue. "On weakly monotonically monolithic spaces." Commentationes Mathematicae Universitatis Carolinae 51.1 (2010): 133-142. <http://eudml.org/doc/37736>.

@article{Peng2010,
abstract = {In this note, we introduce the concept of weakly monotonically monolithic spaces, and show that every weakly monotonically monolithic space is a $D$-space. Thus most known conclusions on $D$-spaces can be obtained by this conclusion. As a corollary, we have that if a regular space $X$ is sequential and has a point-countable $wcs^*$-network then $X$ is a $D$-space.},
author = {Peng, Liang-Xue},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {$D$-space; sequential space; $wcs^*$-network; weakly monotonically monolithic space; -space; sequential space; -network; weakly monotonically monolithic space},
language = {eng},
number = {1},
pages = {133-142},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On weakly monotonically monolithic spaces},
url = {http://eudml.org/doc/37736},
volume = {51},
year = {2010},
}

TY - JOUR
AU - Peng, Liang-Xue
TI - On weakly monotonically monolithic spaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2010
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 51
IS - 1
SP - 133
EP - 142
AB - In this note, we introduce the concept of weakly monotonically monolithic spaces, and show that every weakly monotonically monolithic space is a $D$-space. Thus most known conclusions on $D$-spaces can be obtained by this conclusion. As a corollary, we have that if a regular space $X$ is sequential and has a point-countable $wcs^*$-network then $X$ is a $D$-space.
LA - eng
KW - $D$-space; sequential space; $wcs^*$-network; weakly monotonically monolithic space; -space; sequential space; -network; weakly monotonically monolithic space
UR - http://eudml.org/doc/37736
ER -

References

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