A regular space with a countable network and different dimensions

Delistathis, George; Watson, Stephen

doi:10.1090/S0002-9947-00-02473-9

A regular space with a countable network and different dimensions
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by George Delistathis and Stephen Watson PDF

Trans. Amer. Math. Soc. 352 (2000), 4095-4111 Request permission

Abstract:

In this paper, we construct a regular space with a countable network (even the union of countably many separable metric subspaces) in which $ind$ and $dim$ do not coincide under the assumption of the continuum hypothesis (CH). This gives a consistent negative answer to a question of A.V. Arhangel’skiĭ.

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