Lupianez, Francisco (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.
|Uncontrolled Keywords:||-paracompact subsets; Perfect mappings; Well-situated subsets; Class|
|Subjects:||Sciences > Mathematics > Topology|
|Deposited On:||24 May 2012 11:28|
|Last Modified:||12 Sep 2012 12:55|
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