Torus-like continua which are not self-covering spaces (CROSBI ID 108981)
Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija
Podaci o odgovornosti
Eda, Katsuya ; Mandić, Joško ; Matijević, Vlasta
engleski
Torus-like continua which are not self-covering spaces
For each non-quadratic p-adic integer, p>2, we give an example of a torus-like continuum Y (i.e. inverse limit of an inverse sequence, where each term is the 2-torus T² ; ; ; and each bonding map is a surjective homomorphism), which admits three non-equivalent 4-sheeted coverings f₁ :X₁ → Y, f₂ :X₂ → Y, f₃ :X₃ → Y such that the total spaces X₁ =Y, X₂ and X₃ are pair-wise non-homeomorphic. Furthermore, Y admits a p-sheeted covering f₄ :X₄ → Y, although each bonding map of Y is a p-sheeted covering of T² ; ; ; . In particular, Y is not a self-covering space. This example shows that the class of self-covering spaces is not closed under the operation of forming inverse limits with open surjective bonding maps.
Inverse system; direct system; h-connected space; covering mapping; torus-like continuum; p-adic number; torsion-free group of rank 2; quadratic number.
nije evidentirano
nije evidentirano
nije evidentirano
nije evidentirano
nije evidentirano
nije evidentirano