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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Local degree of separability and invariance of domain


Author: L. B. Treybig
Journal: Proc. Amer. Math. Soc. 34 (1972), 273-279
MSC: Primary 54A25
DOI: https://doi.org/10.1090/S0002-9939-1972-0295278-4
MathSciNet review: 0295278
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Abstract: In $ {E^n}$ an invariance of domain theorem may be proved assuming the Jordan Brouwer Theorem. In this paper such a theorem is proved for various locally compact, connected, Hausdorff spaces which satisfy a certain local degree of separability property. An example shows the separability condition may not be removed. A second theorem yields additional information about homogeneous spaces which satisfy the hypotheses of the first theorem.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0295278-4
Keywords: Invariance of domain, local degree of separability, homogeneous space
Article copyright: © Copyright 1972 American Mathematical Society