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Proceedings of the American Mathematical Society

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

 

 

Homogeneity and Cantor manifolds


Author: Paweł Krupski
Journal: Proc. Amer. Math. Soc. 109 (1990), 1135-1142
MSC: Primary 54F45; Secondary 54C10
DOI: https://doi.org/10.1090/S0002-9939-1990-1009992-7
MathSciNet review: 1009992
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Abstract: Some consequences of generalized homogeneity are observed in dimension theory of metrizable spaces. In particular, if $ X$ is a connected, locally compact, metric space which is homogeneous with respect to open 0-dimensional mappings and if $ \dim X = n \geq 1(\dim X = \infty )$, then no subset of dimension $ \leq n - 2$ (respectively, of a finite dimension) separates $ X$. Thus, homogeneous continua are Cantor manifolds.


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DOI: https://doi.org/10.1090/S0002-9939-1990-1009992-7
Keywords: Homogeneous space, open mapping, finite-dimensional mapping, Cantor manifold, infinite-dimensional space
Article copyright: © Copyright 1990 American Mathematical Society