Classification of locally 2-connected compact metric spaces

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    Abstract

    The aim of this paper is to prove that, for compact metric spaces which do not contain infinite complete graphs, the (strong) property of being "locally 2-dimensional" is guaranteed just by a (weak) local connectivity condition. Specifically, we prove that a locally 2-connected, compact metric space M either contains an infinite complete graph or is surface like in the following sense: There exists a unique surface S such that S and M. contain the same finite graphs. Moreover, M is embeddable in S, that is, M is homeomorphic to a subset of S.
    Original languageEnglish
    JournalCombinatorica
    Volume25
    Issue number1
    Pages (from-to)85-103
    ISSN0209-9683
    DOIs
    Publication statusPublished - 2005

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