Gallego Lupiáñez, Francisco2023-06-202023-06-201988C. E. Aull: Paracompact subsets. Proc. Second Prague. Topological Symposium (1966)45-51. R. Engelking: General Topology. Polish Scientific Publishers, Warszawa, 1977. H. W. Martin: Linearly ordered covers, normality and paracompactness. Top. and its Appl. 12 (1981) 305-313. R. Telgársky: C-scattered and paracompact spaces. Fund. Math. 73 (1971) 59—74. R. Telgársky: Corcerning product ofparacompact spaces. Fund. Math. 74 (1972) 153—159.1572-9141https://hdl.handle.net/20.500.14352/57272Part 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.engjournal articlehttp://www.dml.cz/bitstream/handle/10338.dmlcz/102212/CzechMathJ_38-1988-2_1.pdfhttp://dml.cz/open access515.1-paracompact subsetsWell-situated subsetsTopología1210 Topología