Agarwal, Ravi P.; O’Regan, Donal A note on the Lefschetz fixed point theorem for admissible spaces. (English) Zbl 1089.47040 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) Cited in 1 Document MSC: 47H10 Fixed-point theorems 54H25 Fixed-point and coincidence theorems (topological aspects) Keywords:fixed points; Lefschetz space; admissible sets; compact continuous maps PDF BibTeX XML Cite \textit{R. P. Agarwal} and \textit{D. O'Regan}, Bull. Korean Math. Soc. 42, No. 2, 307--313 (2005; Zbl 1089.47040) Full Text: DOI