The fundamental groups of one-dimensional wild spaces and the Hawaiian earring

Katsuya Eda

    Research output: Contribution to journalArticle

    8 Citations (Scopus)

    Abstract

    Let X be a one-dimensional space which contains a copy C of a circle and let it not be semi-locally simply connected at any point on C. Then the fundamental group of X cannot be embeddable into a free σ-product of n-slender groups, for instance, the fundamental group of the Hawaiian earring. Consequently, any one of the fundamental groups of the Sierpinski gasket, the Sierpinski curve, and the Menger curve is not embeddable into the fundamental group of the Hawaiian earring.

    Original languageEnglish
    Pages (from-to)1515-1522
    Number of pages8
    JournalProceedings of the American Mathematical Society
    Volume130
    Issue number5
    DOIs
    Publication statusPublished - 2002

    Keywords

    • Fundamental group
    • Hawaiian earring
    • Menger curve
    • One-dimensional
    • Sierpinski gasket

    ASJC Scopus subject areas

    • Mathematics(all)
    • Applied Mathematics

    Fingerprint Dive into the research topics of 'The fundamental groups of one-dimensional wild spaces and the Hawaiian earring'. Together they form a unique fingerprint.

  • Cite this