On generalized 3-manifolds which are not homologically locally connected

TL;DR

This paper demonstrates that a classical 3-dimensional generalized manifold by van Kampen is an example of a space that is not homologically locally connected, expanding understanding of such spaces beyond previously known examples.

Contribution

It provides a new example of a 3-dimensional generalized manifold that is not homologically locally connected, distinct from earlier constructed non-HLC manifolds.

Findings

The space $X$ is not locally homeomorphic to any compact metrizable 3-manifold.

$X$ is an example of a generalized manifold that is not HLC.

This expands the class of known non-HLC 3-manifolds.

Abstract

We show that the classical example $X$ of a 3-dimensional generalized manifold constructed by van Kampen is another example of not homologically locally connected (i.e. not HLC) space. This space $X$ is not locally homeomorphic to any of the compact metrizable 3-dimensional manifolds constructed in our earlier paper which are not HLC spaces either.