Author： Smyth M.B. Tsaur R.
Publisher： Springer Publishing Company
ISSN： 0927-2852
Source： Applied Categorical Structures, Vol.11, Iss.1, 2003-02, pp. : 95-116
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Abstract
The main theme of this paper is that almost fixed point properties of discrete structures and fixed point properties of (topological) spaces are interdeducible via a suitable category which contains both graphs and spaces as objects. To carry out the program, we have to consider (almost) fixed points of multifunctions, and for this we need a preliminary discussion of power structures for graphs and simplicial complexes. Specific applications developed are: a “digital convexity” (discrete) version of Kakutani's fixed point theorem for convex-valued multifunctions; and fixed point properties of dendrites in terms of those of finite discrete trees.
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