\(S\)-types of global towers of spaces and exterior spaces
type: Item
instance of: scholarly article
title: \(S\)-types of global towers of spaces and exterior spaces
zbMATH Open document ID: 1183.55002
author: N. E. Zubov
published in: Applied Categorical Structures
publication date: 2009-09-02T00:00:00Z
review text: The proper category of topological spaces and proper maps is the ad'hoc notion for the study of non compact spaces. But this category has not enough limits and colimits and has to be replaced by exterior spaces. This new category is complete, cocomplete, contains the proper category as a full subcategory and has a structure of closed model category. If \(S\) is a set of non-negative integers, there are notions of exterior weak \({\mathbb N}\)-\(S\)-equivalence and of exterior \({\mathbb N}\)-\(S\)-type. In the paper under review, the authors establish an equivalence between the category of \(S\)-types of rayed first countable exterior spaces and the category of \(S\)-types of global towers of pointed spaces. Concrete examples, coming from different choices of \(S\), are given.
reviewed by: Daniel Tanré
Mathematics Subject Classification ID: 55P57
Mathematics Subject Classification ID: 55Q70
Mathematics Subject Classification ID: 54A05
Mathematics Subject Classification ID: 18G55
zbMATH DE Number: 5601498
zbMATH Keywords: exterior space
zbMATH Keywords: proper homotopy
zbMATH Keywords: S-type
zbMATH Keywords: global tower of spaces
zbMATH Keywords: global tower of groups
zbMATH Keywords: categorical group
MaRDI profile type: Publication
full work available at URL: s10485-008-9157-0
OpenAlex ID: W1974406712
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DOI: 10.1007/S10485-008-9157-0
description: scientific article; zbMATH DE number 5601498