A NOTE ON THE LEFSCHETZ FIXED POINT THEOREM FOR ADMISSIBLE SPACES
Copyright policy )A NOTE ON THE LEFSCHETZ FIXED POINT THEOREM FOR ADMISSIBLE SPACES
A Hausdorff topological space \(X\) is said to be a \textit{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 \textit{G. Fournier} and \textit{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.
Fixed-point theorems, Fixed-point and coincidence theorems (topological aspects), fixed points, admissible sets, Lefschetz space, compact continuous maps
Fixed-point theorems, Fixed-point and coincidence theorems (topological aspects), fixed points, admissible sets, Lefschetz space, compact continuous maps
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