About the extension problem for proper maps (Q1088203)

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.