A characterization of spaces with discrete topological fundamental group

Abstract

We offer a counterexample to a theorem in the literature and then repair the theorem as follows: The fundamental group of a locally path connected metric space inherits the discrete topology in a natural way if and only if the underlying space is semilocally simply connected.

5 pages

References in corpus (2)

• The fundamental group of the harmonic archipelago
• The Hawaiian earring group is topologically incomplete

Cited by in corpus (3)

• Topological fundamental groups can distinguish spaces with isomorphic homotopy groups
• The Hawaiian earring group is topologically incomplete
• A monomorphism theorem for the inverse limit of nested retracts