A note on monotone countable paracompactness

Ge Ying; Chris Good

Commentationes Mathematicae Universitatis Carolinae (2001)

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

Abstract

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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.

How to cite

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Ying, 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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  8. Michael E., A note on closed maps and compact sets, Israel J. Math. 2 (1964), 173-176. (1964) Zbl0136.19303MR0177396
  9. Pan C., Monotonically c p spaces, Questions Answers Gen. Topology 15 (1997), 24-32. (1997) Zbl0876.54017MR1442507
  10. Siwiec F., Sequence-covering and countably bi-quotient mappings, Topology Appl. 1 (1971), 143-154. (1971) Zbl0218.54016MR0288737
  11. Tanaka Y., On open finite-to-one maps, Bull. Tokyo Gakugei Univ., Ser. IV 25 (1973), 1-13. (1973) Zbl0355.54008MR0346730
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