Automatic continuity in homeomorphism groups of compact 2-manifolds

2006/04/11 by Christian Rosendal, Rosendal, Christian
Computer Science · Mathematics · #Advanced Topology and Set Theory #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis #math.GR #math.GT

paper · pdf · doi:10.48550/arxiv.math/0604257

arxiv created 2006/04/11 · openalex publication_date 2006/04/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that any homomorphism from the homeomorphism group of a compact 2-manifold, with the compact-open topology, or equivalently, with the topology of uniform convergence, into a separable topological group is automatically continuous.

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