A theory of generalized filters
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Authors
Lynn, Freddie Leroy, Jr.
Subjects
Filters
Compactifications
Realcompactifications
Compactifications
Realcompactifications
Advisors
Weir, Maurice Dean
Date of Issue
1970-06
Date
June 1970
Publisher
Monterey, California ; Naval Postgraduate School
Language
en_US
Abstract
This manuscript is a collection of many of the known results in the theory of generalized filters (ß-filters) as well as an extension of some of the work in this area. The relation of ß-filters to compactifications and realcompactifications is given special attention. Special emphasis is also given to the concept of tracing.
After the necessary preliminaries are disposed of, Section I motivates the study of ß-filters by discussing the collection of zero-sets and then the Wallman compactification. The concept of realcompactification is also mentioned.
Section II introduces the concept of ß-filters and exhibits many of the elementary facts about
these generalized filters. The beginning of Section III deals with the convergence of ß-filters. The Frink or Wallman-type compactification of Tychonoff space is presented in detail. The generalization
of this method in constructing realcompactifications in Tychonoff spaces is also discussed. The section closes with the presentation of some tracing results. Finally , Section IV investigates the concept of ß-continuity.
Type
Thesis
Description
Series/Report No
Department
Mathematics
Organization
Naval Postgraduate School (U.S.)
Identifiers
NPS Report Number
Sponsors
Funder
Format
Citation
Distribution Statement
Approved for public release; distribution is unlimited.
Rights
This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.