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Paracompactness and products

✍ Scribed by Scott W. Williams


Publisher
Elsevier Science
Year
1976
Weight
925 KB
Volume
6
Category
Article
ISSN
0016-660X

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We will characterize metacompactness, subparacompactness and paracompactness of subspaces of products of two ordinal numbers. Using them we will show: (1) For such subspaces, weak submetaLindelΓΆfness, screenability and metacompactness are equivalent. (2) Metacompact subspaces of Ο‰ 2 1 are paracomp

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We study a monotone version of countable paracompactness, MCP, and of countable metacompactness, MCM. These properties are common generalizations of countable compactness and stratifiability and are shown to relate closely to the generalized metric g-functions of Hodel: MCM spaces coincide with Ξ²-sp