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The question of the homotopy invariance of the fixed-point property in the class of compact polyhedra. (Russian) Zbl 0731.55002
The topological space (X,$${\mathcal T})$$ is said to have the fixed-point property if for any continuous mapping $$f:X\to X$$ there exists $$x\in X$$ such that $$x=f(x)$$. It is well-known that the fixed-point property is not invariant under homotopy equivalence in general. The author gives a characterization of invariance of the fixed-point property in the class of compact polyhedra.
##### MSC:
 55M20 Fixed points and coincidences in algebraic topology 55M15 Absolute neighborhood retracts