Discreteness and Homogeneity of the Topological Fundamental Group

2009/04/30 by Jack S. Calcut, John D. McCarthy, Calcut, Jack S. +1 · 2 citations
Mathematics · #Algebraic Topology (math.AT) #FOS: Mathematics #General Topology (math.GN) #math.AT #math.GN

paper · pdf · doi:10.48550/arxiv.0904.4739

8 pages, 2 figures

arxiv created 2009/04/30 · arxiv updated 2009/12/01

Abstract

For a locally path connected topological space, the topological fundamental group is discrete if and only if the space is semilocally simply-connected. While functoriality of the topological fundamental group for arbitrary topological spaces remains an open question, the topological fundamental group is always a homogeneous space.

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• Projective representations on operator algebras
• Comparison of Topologies on Fundamental Groups with Subgroup Topology Viewpoint

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