A note on the Lefschetz fixed point theorem for admissible spaces. (English) Zbl 1089.47040

Agarwal, Ravi P.; O’Regan, Donal

Bull. Korean Math. Soc. 42, No. 2, 307-313 (2005).

A Hausdorff topological space \(X\) is said to be a Lefschetz space provided that, for any compact continuous map \(f: X\to X\), the generalized Lefschetz number \(\Lambda(f)\) is defined and \(\Lambda(f)\neq 0\) implies that \(f\) has a fixed point. By G. Fournier and A. Granas [J. Math. Pures Appl., IX. Sér. 52, 271–283 (1973; Zbl 0294.54034)], it is known that any neighborhood extension space \(X\) for compact spaces is a Lefschetz space. Based on this result, the authors show that some types of admissible spaces are Lefschetz spaces.

Reviewer: In-Sook Kim (München)

MSC:

47H10	Fixed-point theorems
54H25	Fixed-point and coincidence theorems (topological aspects)

Keywords:

fixed points; Lefschetz space; admissible sets; compact continuous maps