A construction of noncontractible simply connected cell-like two-dimensional Peano continua

Katsuya Eda, Umed H. Karimov, Dušan Repovš

    Research output: Contribution to journalArticle

    5 Citations (Scopus)

    Abstract

    Using the topologist sine curve we present a new functorial construction of cone-like spaces, starting in the category of all path-connected topological spaces with a base point and continuous maps, and ending in the subcategory of all simply connected spaces. If one starts from a noncontractible n-dimensional Peano continuum for any n > 0, then our construction yields a simply connected noncontractible (n + l)-dimensional celllike Peano continuum. In particular, starting from the circle double-struck S sign 1, one gets a noncontractible simply connected cell-like 2-dimensional Peano continuum.

    Original languageEnglish
    Pages (from-to)193-203
    Number of pages11
    JournalFundamenta Mathematicae
    Volume195
    Issue number3
    DOIs
    Publication statusPublished - 2007

    Keywords

    • Acyclicity
    • Cell-like set
    • Cone-like space
    • Noncontractible compactum
    • Peano continuum

    ASJC Scopus subject areas

    • Algebra and Number Theory

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