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Alpha-paracompact subsets and well-situated subsets

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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Abstract

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.


Item Type:Article
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
ID Code:15337
References:

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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