Discreteness and Homogeneity of the Topological Fundamental Group

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.

8 pages, 2 figures

References in corpus (2)

• The fundamental group of the harmonic archipelago
• Topological fundamental groups can distinguish spaces with isomorphic homotopy groups