AFPP vs FPP
The authors make an interesting investigation of the approximation of continuous structures (topological spaces) by discrete structures (graphs) examining the relation between fixed point properties for the two types of structures. The main theme of the paper is that almost fixed point properties of discrete structures and fixed point properties of topological spaces are interdeductible via a suitable category which contains both graphs and topological spaces as objects. Specific applications developed are: a ``digital convexity'' version of Kakutani's fixed point theorem and fixed point properties of dendrites in terms of those of finite discrete trees.
scientific article; zbMATH DE number 1925063