On the covering dimension of subspaces of product of Sorgenfrey lines

Fora, Ali A.

doi:10.1090/S0002-9939-1978-0509262-1

On the covering dimension of subspaces of product of Sorgenfrey lines
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by Ali A. Fora PDF

Proc. Amer. Math. Soc. 72 (1978), 601-606 Request permission

Abstract:

Let S denote the Sorgenfrey line. Then the following results are proved in this paper: (i) If X is a nonempty subspace of ${S^{{\aleph _0}}}$, then $\dim X = 0$. (ii) For any nonempty separable space $X \subset {S^{{\aleph _0}}},\dim {X^m} = 0$ for any cardinal m.

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