Spaces Of Dimension Zero Academic Article uri icon

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abstract

  • 1. Introduction. In a recent paper (1) it was remarked that the theory of zero-dimensional spaces is exactly that part of general topology which can be described in terms of equivalence relations. Here, it will be shown how this idea can be used to obtain the following characterizations of certain types of zero-dimensional spaces:Any compact zero-dimensional space which has a denumerable basis for its open sets and is dense in itself is homeomorphic to the space of 2-adic integers.

publication date

  • 1957