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A note on monotone countable paracompactness. (English) Zbl 1090.54504

Summary: We show that a space is MCP (monotone countable paracompact) if and only if it has property \((*)\), introduced by H. Teng, S. Xia and S. 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.

MSC:

54C10 Special maps on topological spaces (open, closed, perfect, etc.)
54D20 Noncompact covering properties (paracompact, Lindelöf, etc.)
54E20 Stratifiable spaces, cosmic spaces, etc.
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