A compactness preserving topology for products sets

UNCG Author/Contributor (non-UNCG co-authors, if there are any, appear on document)
Thomas Lavern Howe (Creator)
The University of North Carolina at Greensboro (UNCG )
Web Site: http://library.uncg.edu/
Hughes Hoyle

Abstract: The purpose of this thesis is to investigate the properties of certain topologies for a countable product of lattice isomorphic factor spaces. The idea of using lattice isomorphisms between factors to define a topology on a product space is due to Goolsby in [4]. Both the usual and box topologies are well known. The saturating topology was originated by the author in an effort to describe a topology properly containing the usual topology, but still preserving compactness. The example showing that regualrity of the factor spaces does not guarantee regularity of the saturating topology is also due to Goolsby in a paper not published at the time of this writing. The result that connectivity of the factor spaces does not gaurantee connectivity of the box topology was first proved by Knight in [5], but the proof given here is due to Professor Jerry E. Vaughan of the University of North Carolina at Greensboro. A working knowlege of set theory and elementary topology is assuned. The reader is referred to [13, C2 3, and [3] for definitions and results not covered in this thesis.

Additional Information

Language: English
Date: 1975
Set theory

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