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

Volume 195 / 2007

Katsuya Eda, Umed H. Karimov, Dušan Repovš Fundamenta Mathematicae 195 (2007), 193-203 MSC: Primary 54F15, 54G15, 57N60; Secondary 54C55, 55M15, 55Q52. DOI: 10.4064/fm195-3-1


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 $(n + 1)$-dimensional cell-like Peano continuum. In particular, starting from the circle $\mathbb{S}^1$, one gets a noncontractible simply connected cell-like 2-dimensional Peano continuum.


  • Katsuya EdaSchool of Science and Engineering
    Waseda University
    Tokyo 169-8555, Japan
  • Umed H. KarimovInstitute of Mathematics
    Academy of Sciences of Tajikistan
    Ul. Ainy 299A
    Dushanbe 734063, Tajikistan
  • Dušan RepovšInstitute of Mathematics, Physics and Mechanics
    University of Ljubljana
    P.O. Box 2964
    Ljubljana 1001, Slovenia

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