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Moore's theorem

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arxiv 1001.5140 v1 pith:63HKMHYX submitted 2010-01-28 math.DS math.GN

Vladlen Timorin This is my paper · ORCID
classification math.DSmath.GN
keywords mooretheoremtheoryapplicationsequivalenceproofspherealthough
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In this (mostly expository) paper, we review a proof of the following old theorem of R.L. Moore: for a closed equivalence relation on the 2-sphere such that all equivalence classes are connected and non-separating, and not all points are equivalent, the quotient space is homeomorphic to the 2-sphere. The proof uses a general topological theory close to but simpler than an original theory of Moore. The exposition is organized so that to make applications of Moore's theory (not only Moore's theorem) in complex dynamics easier, although no dynamical applications are mentioned here.

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  1. Topology of two-dimensional collapsed spaces with lower Ricci bounds

    math.DG 2026-06 unverdicted novelty 6.0 of 10

    Collapsed metric measure spaces with lower Ricci bounds and essential dimension two are topological surfaces possibly with boundary.

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