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 𝕊¹, one gets a noncontractible simply connected cell-like 2-dimensional Peano continuum.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm195-3-1,
author = {Katsuya Eda and Umed H. Karimov and Du\v san Repov\v s},
title = {A construction of noncontractible simply connected cell-like two-dimensional Peano continua},
journal = {Fundamenta Mathematicae},
volume = {193},
year = {2007},
pages = {193-203},
zbl = {1148.54016},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm195-3-1}
}
Katsuya Eda; Umed H. Karimov; Dušan Repovš. A construction of noncontractible simply connected cell-like two-dimensional Peano continua. Fundamenta Mathematicae, Tome 193 (2007) pp. 193-203. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm195-3-1/