%0 Journal Article
%A Gallego Lupiáñez, Francisco
%T Alpha-paracompact subsets and well-situated subsets.
%D 1987
%@ 0918-4732
%U https://hdl.handle.net/20.500.14352/64621
%X 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 toTamano’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.
%~