Homogeneity and Cantor manifolds
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- by Paweł Krupski PDF
- Proc. Amer. Math. Soc. 109 (1990), 1135-1142 Request permission
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.References
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Additional Information
- © Copyright 1990 American Mathematical Society
- 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