Alpha-paracompact subsets and well-situated subsets.



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Lupianez, Francisco Gallego (1987) Alpha-paracompact subsets and well-situated subsets. Questions and answers in general topology , 5 . pp. 293-302. ISSN 0918-4732


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.

Item Type:Article
Uncontrolled Keywords:-paracompact subsets; Perfect mappings; Well-situated subsets; Class
Subjects:Sciences > Mathematics > Topology
ID Code:15340
Deposited On:24 May 2012 09:28
Last Modified:12 Dec 2018 15:13

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