Lupianez, Francisco (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.
|Additional Information:||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 11:49|
|Last Modified:||24 May 2012 11:49|
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