Prime subspaces in free topological groups

Katsuya Eda, Haruto Ohta, Kohzo Yamada

    Research output: Contribution to journalArticle

    9 Citations (Scopus)

    Abstract

    Let F(X) (A(X)) be the free (Abelian) topological group over X. We prove: If P is one of the spaces R, Q, R, Q, βω, βω ω and 2/gk for an infinite κ and if F(X) or A(X) contains a copy of P, then X contains a copy of P. If P is the one-point compactification of an infinite discrete space or ω1 + 1, this is not true. If P = ω1, this holds for F(X) but is independent of ZFCfor A(X).

    Original languageEnglish
    Pages (from-to)163-171
    Number of pages9
    JournalTopology and its Applications
    Volume62
    Issue number2
    DOIs
    Publication statusPublished - 1995 Mar 24

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    Keywords

    • Convergent sequenc
    • Free Abelian topological group
    • Free topological group
    • Prime space
    • Self-embeddable space
    • Symmetric product

    ASJC Scopus subject areas

    • Geometry and Topology

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