Lupianez, Francisco Gallego (1988) Alpha-paracompact subsets and well-situated subsets. Czechoslovak Mathematical Journal , 38 (2). pp. 191-197. ISSN 1572-9141
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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.
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.
|Uncontrolled Keywords:||-paracompact subsets; Well-situated subsets|
|Subjects:||Sciences > Mathematics > Topology|
C. 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.
|Deposited On:||24 May 2012 09:49|
|Last Modified:||06 Feb 2014 10:22|
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