On covering dimension and inverse limits of compact spaces

1960/06/01 by Sibe Mardešić · 7 citations
Computer Science · Mathematics · #Advanced Topology and Set Theory #Digital Image Processing Techniques #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.1215/ijm/1255455869

crossref issued 1960/06/01 · crossref published 1960/06/01 · crossref published-print 1960/06/01 · openalex publication_date 1960/06/01 · crossref created 2019/03/04 · crossref deposited 2024/01/30 · openalex created_date 2025/10/10 · crossref indexed 2026/07/25 · openalex updated_date 2026/07/25

Abstract

In 1937 H. Freudenthal proved that every metrizable compact space X is homeomorphic with the inverse limit of an inverse sequence of compact polyhedra P, whose dimension dim P __< dim X ([3], Satz 1, p. 229). In this paper we ourselves propose to generalize Freudenthal's theorem to the case of Hausdorff compact spaces. Throughout the paper dimension is taken in the sense of finite open coverings and is denoted by dim.

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