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Proceedings of the American Mathematical Society

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

 
 

 

On the existence of totally inhomogeneous spaces


Author: Brian M. Scott
Journal: Proc. Amer. Math. Soc. 51 (1975), 489-493
MSC: Primary 54F50
DOI: https://doi.org/10.1090/S0002-9939-1975-0375262-5
MathSciNet review: 0375262
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Abstract: A property of total inhomogeneity for topological spaces is defined and is shown to be stronger than that of rigidity (i.e., of having trivial autohomeomorphism group). It is further shown that compact, rigid, Hausdorff spaces are totally inhomogeneous, and that totally inhomogeneous spaces exist in profusion as dense subspaces of a class of locally compact spaces.


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DOI: https://doi.org/10.1090/S0002-9939-1975-0375262-5
Keywords: Rigid space, totally inhomgeneous space, locally compact space
Article copyright: © Copyright 1975 American Mathematical Society

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