Vol. 92, No. 2, 1981

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On the structure of hyper-real z-ultrafilters

James Glenn Brookshear

Vol. 92 (1981), No. 2, 269–275

This paper investigates the structure of hyper-real z-ultrafilters on completely regular, Hausdorff spaces in an attempt to describe their structure in manageable terms. A consequence of this investigation is a scheme for classifying these z-filters based on the complexity of their structure. It is shown that the real numbers with the usual topology exhibit hyper-real z-ultrafilters within each category of the classification. The paper closes with a discussion of how the action of z-filters in one category influence those in the other categories with particular applications to the study of C(X).

Mathematical Subject Classification 2000
Primary: 54A25
Secondary: 54D35
Received: 16 March 1979
Revised: 7 August 1979
Published: 1 February 1981
James Glenn Brookshear