\(S\)-types of global towers of spaces and exterior spaces
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.
scientific article; zbMATH DE number 5601498
scientific article