About the extension problem for proper maps
type: Item
instance of: scholarly article
title: About the extension problem for proper maps
zbMATH Open document ID: 0612.55021
DOI: 10.1016/0166-8641(87)90074-5
published in: Topology and its Applications
publication date: 1987-01-01T00:00:00Z
review text: Obstruction theory [see \textit{S.-T. Hu}, Homotopy Theory (1959; Zbl 0088.388)], is a useful construction in classical algebraic topology for studying the extension problem for continuous maps. This paper defines an analogous obstruction theory which is useful for studying the extension problem for proper maps. Recall that a continuous map \(f: X\to Y\) is proper if \(f^{-1}(K)\) is compact for every compact subset K of Y. As an application, an analogue of Eilenberg's extension theorem (loc.cit.) is proved for proper maps. Many other results analogous to the classical results are also given. These results are somewhat too technical to state in this review; however, they are quite interesting for a worker in the proper category.
Mathematics Subject Classification ID: 55S36
Mathematics Subject Classification ID: 55S35
zbMATH DE Number: 3990397
zbMATH Keywords: proper obstruction cycle
zbMATH Keywords: proper cohomology
zbMATH Keywords: extension problem for proper maps
author: L. Javier Hernández
reviewed by: Sukhjit Singh
MaRDI profile type: Publication
full work available at URL: 0166-8641(87)90074-5
OpenAlex ID: W2050878853
cites work: Etale homotopy
cites work: Cohomology and continuous mappings
cites work: Cech and Steenrod homotopy theories with applications to geometric topology
cites work: Q5802788
cites work: Q3959112
cites work: Q4169424
cites work: Q5825483
description: scientific article; zbMATH DE number 3990397