Torus-like continua which are not self-covering spaces

Katsuya Eda, Joško Mandić, Vlasta Matijević

    Research output: Contribution to journalArticle

    7 Citations (Scopus)

    Abstract

    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 4-sheeted covering maps f0: X0 → Y, f1: X1 → Y, f2: X2 → Y such that the total spaces and X0 = Y, X2 are pair-wise non-homeomorphic. Furthermore, Y admits a 2p-sheeted covering map f3: X3 → Y such that X3 and Y are non-homeomorphic. 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.

    Original languageEnglish
    Pages (from-to)359-369
    Number of pages11
    JournalTopology and its Applications
    Volume153
    Issue number2-3 SPEC. ISS.
    DOIs
    Publication statusPublished - 2005 Sep 1

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    Keywords

    • Covering mapping
    • Direct system
    • H-connected space
    • Inverse system
    • p-adic number
    • Quadratic number
    • Torsion-free group of rank 2
    • Torus-like continuum

    ASJC Scopus subject areas

    • Geometry and Topology

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