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

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