On measure homology of mildly wild spaces

TL;DR

This paper demonstrates that for specific 'mildly wild' spaces with countable fundamental groups, the canonical map from singular homology to measure homology is injective, expanding understanding of homology theories in complex spaces.

Contribution

It establishes the injectivity of the canonical map from singular to measure homology for a new class of spaces not homotopy equivalent to CW-complexes.

Findings

Injectivity of the canonical map proven for certain spaces

Spaces considered have countable fundamental groups

Extends homology theory applicability to 'mildly wild' spaces

Abstract

We prove injectivity of the canonical map from singular homology to measure homology for certain ``mildly wild" spaces, that is, certain spaces not having the homotopy type of a CW-complex, but having countable fundamental groups.