On a problem of simultaneous quasi-uniform extension

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Abstract

Let T be a topology on a set X and X = ∪1n Xi, Xi ∩ Xj = ∅ (i ≠ j), Ui, a quasi-uniformity on Xi (i = 1,..., n). The paper establishes necessary and sufficient conditions for the existence of a quasi-uniformity U on X with the property that the topology induced by U coincides with T and the restriction of U to Xi is equal to Ui. The rather complicated condition in the general case can be simplified in the special case n = 2.

Original languageEnglish
Pages (from-to)173-186
Number of pages14
JournalActa Mathematica Hungarica
Volume82
Issue number3
DOIs
Publication statusPublished - Feb 1999

ASJC Scopus subject areas

  • Mathematics(all)

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