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Alpha-paracompact subsets and well-situated subsets Gallego Lupiáñez, Francisco 515.1 -paracompact subsets Well-situated subsets Topología 1210 Topología Part of this paper is contained in the author's Doctoral Thesis written under the supervisionofProfessor E.Outerelo. Thispaper has been publishedinashorted version in Quest.& Ans. Gen. Topology 5 (1987), 293-302. In this paper -paracompact and well-situated subsets are further examined. A subset E of a space X is paracompact if every covering of E by open sets has a refinement by open sets, locally finite in X, which covers E [C. E. Aull, Proc. 2nd Prague Topol. Symp. 1966, 45-51 (1967; Zbl 0162.264)] and is well-situated in X if for every paracompact T2 space Y, E × Y is -paracompact in X × Y [H. W. Martin, Topology Appl.12, 305-313 (1981; Zbl 0483.54011)]. Covering properties of -paracompact and wellsituated ubsets are obtained, -paracompact and well-situated subsets are characterizedin regular spaces, the behavior of paracompact and well-situated subsets under perfect mappings is studied, and it is shown that the class of all paracompact T2 spaceswhich are well-situated in every paracompact T2 space in which they are embedded as closed subsets, is perfect. Depto. de Álgebra, Geometría y Topología Fac. de Ciencias Matemáticas TRUE pub 2023-06-20T16:52:01Z 2023-06-20T16:52:01Z 1988 journal article https://hdl.handle.net/20.500.14352/57272 1572-9141 eng open access application/pdf Institute of Mathematics, Czech Academy of Sciences