# A note on monotone countable paracompactness

Commentationes Mathematicae Universitatis Carolinae (2001)

- Volume: 42, Issue: 4, page 771-778
- ISSN: 0010-2628

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topYing, Ge, and Good, Chris. "A note on monotone countable paracompactness." Commentationes Mathematicae Universitatis Carolinae 42.4 (2001): 771-778. <http://eudml.org/doc/248762>.

@article{Ying2001,

abstract = {We show that a space is MCP (monotone countable paracompact) if and only if it has property $(*)$, introduced by Teng, Xia and Lin. The relationship between MCP and stratifiability is highlighted by a similar characterization of stratifiability. Using this result, we prove that MCP is preserved by both countably biquotient closed and peripherally countably compact closed mappings, from which it follows that both strongly Fréchet spaces and q-space closed images of MCP spaces are MCP. Some results on closed images of wN spaces are also noted.},

author = {Ying, Ge, Good, Chris},

journal = {Commentationes Mathematicae Universitatis Carolinae},

keywords = {monotone countable paracompactness; MCP; monotone countable metacompactness; MCM; $\beta $-space; wN-space; g-functions; stratifiability; countably biquotient mapping; peripherally countably compact mapping; (quasi-)perfect mapping; monotone countable paracompactness; MCP; monotone countable metacompactness; MCM; -space; -space; -functions},

language = {eng},

number = {4},

pages = {771-778},

publisher = {Charles University in Prague, Faculty of Mathematics and Physics},

title = {A note on monotone countable paracompactness},

url = {http://eudml.org/doc/248762},

volume = {42},

year = {2001},

}

TY - JOUR

AU - Ying, Ge

AU - Good, Chris

TI - A note on monotone countable paracompactness

JO - Commentationes Mathematicae Universitatis Carolinae

PY - 2001

PB - Charles University in Prague, Faculty of Mathematics and Physics

VL - 42

IS - 4

SP - 771

EP - 778

AB - We show that a space is MCP (monotone countable paracompact) if and only if it has property $(*)$, introduced by Teng, Xia and Lin. The relationship between MCP and stratifiability is highlighted by a similar characterization of stratifiability. Using this result, we prove that MCP is preserved by both countably biquotient closed and peripherally countably compact closed mappings, from which it follows that both strongly Fréchet spaces and q-space closed images of MCP spaces are MCP. Some results on closed images of wN spaces are also noted.

LA - eng

KW - monotone countable paracompactness; MCP; monotone countable metacompactness; MCM; $\beta $-space; wN-space; g-functions; stratifiability; countably biquotient mapping; peripherally countably compact mapping; (quasi-)perfect mapping; monotone countable paracompactness; MCP; monotone countable metacompactness; MCM; -space; -space; -functions

UR - http://eudml.org/doc/248762

ER -

## References

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