Publication: Alpha-paracompact subsets and well-situated subsets.
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1987
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Symposium of General Topology
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Abstract
We study -paracompact subsets, defined by C. E. Aull. Here we obtain some covering properties of -paracompact subsets which are similar to properties of paracompact spaces. In particular, we characterize -paracompact subsets in regular spaces. Moreover we study the behaviour of -paracompact subsets under perfect mappings.
Then we consider R. Telg´arsky’s well-situated subsets. The properties of -paracompact subsets yield properties of well-situated subsets. Well-situated subsets are related to
Tamano’s problem (i.e.: to give an intrinsic description of those T2 spaces X such that X × Y is paracompact for each paracompact T2 space Y) which remains open.
Finally, we solve a problem of Telg´arsky establishing that: In the realm of T2 spaces,the class is perfect.