On homologically locally connected spaces

Akira Koyama; Vesko Valov

doi:10.1016/j.topol.2019.03.012

On homologically locally connected spaces

Akira Koyama, Vesko Valov

School of Fundamental Science and Engineering

Research output: Contribution to journal › Article › peer-review

Abstract

We provide some properties and characterizations of homologically UV ⁿ -maps and lc _G ⁿ -spaces. We show that there is a parallel between recently introduced by Cauty [3] algebraic ANR's and homologically lc _G ⁿ -metric spaces, and this parallel is similar to the parallel between ordinary ANR's and LC ⁿ -metric spaces. We also show that there is a similarity between the properties of LC ⁿ -spaces and lc _G ⁿ -spaces. Some open questions are raised.

Original language	English
Pages (from-to)	57-69
Number of pages	13
Journal	Topology and its Applications
Volume	260
DOIs	https://doi.org/10.1016/j.topol.2019.03.012
Publication status	Published - 2019 Jun 15

Keywords

Fixed points
Homological UV sets
Homological selections

ASJC Scopus subject areas

Geometry and Topology

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10.1016/j.topol.2019.03.012

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@article{5732f8d1a6204e498acfb05592ff6c3a,

title = "On homologically locally connected spaces",

abstract = " We provide some properties and characterizations of homologically UV n -maps and lc G n -spaces. We show that there is a parallel between recently introduced by Cauty [3] algebraic ANR's and homologically lc G n -metric spaces, and this parallel is similar to the parallel between ordinary ANR's and LC n -metric spaces. We also show that there is a similarity between the properties of LC n -spaces and lc G n -spaces. Some open questions are raised. ",

keywords = "Fixed points, Homological UV sets, Homological selections",

author = "Akira Koyama and Vesko Valov",

note = "Funding Information: The author was partially supported by Grant-in-Aid for Scientific Research (C) 16K05160.The author was partially supported by NSERC Grant 261914-13.",

year = "2019",

month = jun,

day = "15",

doi = "10.1016/j.topol.2019.03.012",

language = "English",

volume = "260",

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journal = "Topology and its Applications",

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T1 - On homologically locally connected spaces

AU - Koyama, Akira

AU - Valov, Vesko

N1 - Funding Information: The author was partially supported by Grant-in-Aid for Scientific Research (C) 16K05160.The author was partially supported by NSERC Grant 261914-13.

PY - 2019/6/15

Y1 - 2019/6/15

N2 - We provide some properties and characterizations of homologically UV n -maps and lc G n -spaces. We show that there is a parallel between recently introduced by Cauty [3] algebraic ANR's and homologically lc G n -metric spaces, and this parallel is similar to the parallel between ordinary ANR's and LC n -metric spaces. We also show that there is a similarity between the properties of LC n -spaces and lc G n -spaces. Some open questions are raised.

AB - We provide some properties and characterizations of homologically UV n -maps and lc G n -spaces. We show that there is a parallel between recently introduced by Cauty [3] algebraic ANR's and homologically lc G n -metric spaces, and this parallel is similar to the parallel between ordinary ANR's and LC n -metric spaces. We also show that there is a similarity between the properties of LC n -spaces and lc G n -spaces. Some open questions are raised.

KW - Fixed points

KW - Homological UV sets

KW - Homological selections

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