Maximally connected topological spaces

UNCG Author/Contributor (non-UNCG co-authors, if there are any, appear on document)
Andrew Kelly Garner (Creator)
The University of North Carolina at Greensboro (UNCG )
Web Site:
Karl Gentry

Abstract: A connected topological space is called maximally connected if every proper expansion of this space is disconnected. The purpose of this thesis is to investigate the existance of and the properties of maximally connected topological spaces. For many years it was unknown whether or not there existed maximally connected Hausdorff spaces. Particular interest concerning maximally connected Hausdorff spaces settled around the existance of a maximally connected expansion of the usual topology on the set of real numbers. Recently, in fact during the writing of this thesis, this problem was solved independently by J. A. Guthrie, H. E. Stone, and Wage. All three men have constructed examples of maximally connected Hausdorff spaces. Regretably, none of these have been published at the time of this writing.

Additional Information

Language: English
Date: 1976
Topological spaces

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