Homeomorphic subspaces in the plane

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

Abstract: The idea of topological equivalence, or homeomorphic, is one of the basic considerations in any study of topology. Mrs. Yandell [3], in her master's thesis, compared pairs of spaces in the plane to determine whether or not they were homeomorphic. Decisions as to whether or not a pair of spaces were homeomorphic were based on several topological properties, including compactness and connectedness. In this thesis three additional topological properties are defined and used for the purpose of increasing the number of decisions that could be made with only the topological properties discussed in [33- In Chapter I, locally compact is defined and general theorems are proved concerning this property. In addition localy compactness is shown to be a topological property. In Chapter II, locally connected is defined, general theorems are proved, and local connectedness is shown to be a topological property. In Chapter III, connected im kleinen is defined, related to local connectedness, and shown to be a topological property. In Chapter IV, examples are given to show that indeed the studies in [3] have been extended.

Additional Information

Language: English
Date: 1972
Topological spaces
Locally compact spaces

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