A topology on homotopy set induced by pairings - Oda, Nobuyuki; Yamaguchi, Toshihiro (Topology Proceedings, 2024)
Pairings of based topological spaces define perpendicular relations among base point preserving continuous maps. A topology on a base point preserving homotopy set is defined by making use of the perpendicular relation. The topological space thus obtained is an Alexandroff space. Some conditions are obtained for the induced function to be continuous. The dual results are also studied on the basis of copairings. Rational examples due to Arkowitz and Lupton whose homotopy classes of selfmaps are finite sets are studied in detail.