engleski

Finite-sheeted covering maps from and over 2-dimensional compact connested abelian groups

Let G be a compact connected 2-dimensional Abelian group, i.e. the inverse limit of an inverse sequence, where each term is 2-torus and each bonding map is a finite-sheeted covering homomorphism over 2-torus. Using the classification theorem for finite-sheeted covering maps over connected paracompact spaces, we classify finite-sheeted covering maps (with connected total spaces) over G and investigate total spaces up to homeomorphism. In particular, we show that the class of self-covering spaces is not closed under the operation of forming inverse limits with open surjective bonding maps, since there is a 2-dimensional compact connected Abelian group, which is not a self-covering space. We also study finite-sheeted covering maps from G to other compact connected spaces Y. For that purpose we classify finite-sheeted covering maps over Klein bottle-like continua Σ (p, q, r) introduced by C. Tezer.

Compact abelian group; 2-dimensional; finite-sheeted covering map

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