Vol. 49, No. 1, 1973

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Paracompactifications using filter bases

James D. Wine

Vol. 49 (1973), No. 1, 285–304

During the mid nineteen sixties, C. E. Aull presented a series of papers in which he distinguished several different types of paracompact subsets. Using these concepts, three classes of filter bases are introduced and their convergence and other properties are studied. A variety of characterizations of paracompactness based on the existence of certain types of these filter bases and z-filters are given. A paracompactification construction involving the addition of limit points for one of the classes of filter bases is presented in detail. Finally, properties of the paracompactification are explored with some attention given to its ring of continuous functions.

Mathematical Subject Classification 2000
Primary: 54C30
Secondary: 54D20
Received: 14 July 1972
Revised: 5 April 1973
Published: 1 November 1973
James D. Wine