Borsuk's quasi-equivalence is not transitive
Andrzej Kadlof ; Nikola Koceić Bilan ; Nikica Uglešić
Fundamenta Mathematicae, Tome 193 (2007), p. 215-227 / Harvested from The Polish Digital Mathematics Library
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Borsuk's quasi-equivalence relation on the class of all compacta is considered. The open problem concerning transitivity of this relation is solved in the negative. Namely, three continua X, Y and Z lying in ℝ³ are constructed such that X is quasi-equivalent to Y and Y is quasi-equivalent to Z, while X is not quasi-equivalent to Z.

Publié le : 2007-01-01
EUDML-ID : urn:eudml:doc:286070 
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     title = {Borsuk's quasi-equivalence is not transitive},
     journal = {Fundamenta Mathematicae},
     volume = {193},
     year = {2007},
     pages = {215-227},
     zbl = {1144.54011},
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Andrzej Kadlof; Nikola Koceić Bilan; Nikica Uglešić. Borsuk's quasi-equivalence is not transitive. Fundamenta Mathematicae, Tome 193 (2007) pp. 215-227. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm197-0-9/