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

Katsuya Eda¹ ; Umed H. Karimov² ; Dušan Repovš³

¹ School of Science and Engineering Waseda University Tokyo 169-8555, Japan
² Institute of Mathematics Academy of Sciences of Tajikistan Ul. Ainy 299A Dushanbe 734063, Tajikistan
³ Institute of Mathematics, Physics and Mechanics University of Ljubljana P.O. Box 2964 Ljubljana 1001, Slovenia

Fundamenta Mathematicae, Tome 195 (2007) no. 3, pp. 193-203

Résumé

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.

Détail

DOI : 10.4064/fm195-3-1

Keywords: using topologist sine curve present functorial construction cone like spaces starting category path connected topological spaces base point continuous maps ending subcategory simply connected spaces starts noncontractible n dimensional peano continuum construction yields simply connected noncontractible dimensional cell like peano continuum particular starting circle mathbb gets noncontractible simply connected cell like dimensional peano continuum