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Abstract <p>It is proved that a finally compact <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(p\)</EquationSource> <!--BMatMGU2570067Kombarov-m1--> </InlineEquation>-space is metrizable iff the space <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(X^{2}\setminus\Delta\)</EquationSource> <!--BMatMGU2570067Kombarov-m2--> </InlineEquation> has a countable rectangular open cover. A similar theorem is valid for separable <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(M\)</EquationSource> <!--BMatMGU2570067Kombarov-m3--> </InlineEquation>-spaces.</p>

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A Remark about Countable Rectangular Covers outside the Diagonal

  • 期刊论文

  • 发表日期：

    2025年12月1日

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  • A. P. Kombarov

摘要

Abstract

It is proved that a finally compact \(p\) -space is metrizable iff the space \(X^{2}\setminus\Delta\) has a countable rectangular open cover. A similar theorem is valid for separable \(M\) -spaces.