On homologically locally connected spaces

Akira Koyama; Vesko Valov

paper

On homologically locally connected spaces

arXiv:1712.04125

Abstract

We provide some properties and characterizations of homologically $U V^{n}$ -maps and $l c_{G}^{n}$ -spaces. We show that there is a parallel between recently introduced by Cauty algebraic $A N R$ 's and homologically $l c_{G}^{n}$ -metric spaces, and this parallel is similar to the parallel between ordinary $A N R$ 's and $L C^{n}$ -metric spaces. We also show that there is a similarity between the properties of $L C^{n}$ -spaces and $l c_{G}^{n}$ -spaces. Some open questions are raised.

20 pages