Singular multivalued homology

TL;DR

The paper proves that the multivalued analogue of singular homology vanishes for all positive degrees in compact, Hausdorff spaces, extending known results for the case n=1.

Contribution

It establishes the vanishing of multivalued singular homology groups for all positive degrees in compact, Hausdorff spaces, generalizing previous specific cases.

Findings

Multivalued singular homology groups are zero for all n > 0 in compact, Hausdorff spaces.

The case n=1 was previously known and now extended to all n > 0.

Provides a comprehensive understanding of multivalued homology in topological spaces.

Abstract

Let $X$ be a compact, Hausdorff topological space. Then $H^M_n(X)=0$ for all $n>0$, where $H_n$ is the multivalued analogue of singular homology. The case $n=1$ is already known [8].