## 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)

Zbl 0294.54034
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