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One-dimensional Peano continua with zero-dimensional wild part

Volume 259 / 2022

Katsuya Eda Fundamenta Mathematicae 259 (2022), 243-253 MSC: Primary 55P10; Secondary 55P15, 54F50, 05C10, 05C99. DOI: 10.4064/fm41-1-2022 Published online: 4 July 2022


Let $X^w$ be the subspace of a space $X$ consisting of all points at which $X$ is not semi-locally simply connected. Let $X$ be a one-dimensional Peano continuum. It is known that if $X^w$ is one point, then $X$ is homotopy equivalent to the Hawaiian earring. However, the homeomorphism type of $X^w$ does not determine the homotopy type of $X$ in general. Here, we show that, for a one-dimensional Peano continuum $X$ such that $X^w$ is zero-dimensional and non-empty, the homeomorphism type of $X^w$ determines the homotopy type of $X$.


  • Katsuya EdaDepartment of Mathematics
    Waseda University
    Tokyo 169-8555, Japan

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