1School of Science and Engineering Waseda University Tokyo 169-8555, Japan 2Institute of Mathematics Academy of Sciences of Tajikistan Ul. Ainy 299A Dushanbe 734063, Tajikistan 3Institute 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
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.
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
Affiliations des auteurs :
Katsuya Eda
1
;
Umed H. Karimov
2
;
Dušan Repovš
3
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
@article{10_4064_fm195_3_1,
author = {Katsuya Eda and Umed H. Karimov and Du\v{s}an Repov\v{s}},
title = {A construction of noncontractible simply connected cell-like
two-dimensional {Peano} continua},
journal = {Fundamenta Mathematicae},
pages = {193--203},
year = {2007},
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doi = {10.4064/fm195-3-1},
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AU - Umed H. Karimov
AU - Dušan Repovš
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%J Fundamenta Mathematicae
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Katsuya Eda; Umed H. Karimov; Dušan Repovš. A construction of noncontractible simply connected cell-like
two-dimensional Peano continua. Fundamenta Mathematicae, Tome 195 (2007) no. 3, pp. 193-203. doi: 10.4064/fm195-3-1
