Torus-like continua which are not self-covering spaces

Katsuya Eda, Joško Mandić, Vlasta Matijević

    Research output: Contribution to journalArticle

    6 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

    Fingerprint

    Covering Map
    Covering Space
    Inverse Limit
    Torus
    Continuum
    P-adic
    Homomorphism
    Closed
    Integer
    Term
    Class

    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

    Cite this

    Torus-like continua which are not self-covering spaces. / Eda, Katsuya; Mandić, Joško; Matijević, Vlasta.

    In: Topology and its Applications, Vol. 153, No. 2-3 SPEC. ISS., 01.09.2005, p. 359-369.

    Research output: Contribution to journalArticle

    Eda, K, Mandić, J & Matijević, V 2005, 'Torus-like continua which are not self-covering spaces', Topology and its Applications, vol. 153, no. 2-3 SPEC. ISS., pp. 359-369. https://doi.org/10.1016/j.topol.2003.06.006
    Eda, Katsuya ; Mandić, Joško ; Matijević, Vlasta. / Torus-like continua which are not self-covering spaces. In: Topology and its Applications. 2005 ; Vol. 153, No. 2-3 SPEC. ISS. pp. 359-369.
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