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December 2006 Subspaces of the Sorgenfrey line and their products
Vitalij A. Chatyrko
Tsukuba J. Math. 30(2): 401-413 (December 2006). DOI: 10.21099/tkbjm/1496165070

Abstract

In this article we study the products of subspaces of the Sorgenfrey line 9. Using an idea by D. K. Burke and J. T. Moore[2] we prove in particular the following: Let $X_{i}, i = 1, \ldots ,n, n \geq 1$, be subspaces of $\mathscr{S}$, where each $X_i$ is uncountable. Then $X_{1} \times \ldots \times X_{n} \times x \mathscr{Q}$ can be embedded in $\mathscr{S}^{n+1}$ but can not be embedded in $\mathscr{S}^{n}$, where $\mathscr{Q}$ is the space of rational numbers with the natural topology. This statement strengthens [2, Theorem 2.1].

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Vitalij A. Chatyrko. "Subspaces of the Sorgenfrey line and their products." Tsukuba J. Math. 30 (2) 401 - 413, December 2006. https://doi.org/10.21099/tkbjm/1496165070

Information

Published: December 2006
First available in Project Euclid: 30 May 2017

zbMATH: 1119.54023
MathSciNet: MR2271307
Digital Object Identifier: 10.21099/tkbjm/1496165070

Rights: Copyright © 2006 University of Tsukuba, Institute of Mathematics

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Vol.30 • No. 2 • December 2006
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