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Fixed-point property : ウィキペディア英語版
Fixed-point property
A mathematical object ''X'' has the fixed-point property if every suitably well-behaved mapping from ''X'' to itself has a fixed point. The term is most commonly used to describe topological spaces on which every continuous mapping has a fixed point. But another use is in order theory, where a partially ordered set ''P'' is said to have the fixed point property if every increasing function on ''P'' has a fixed point.
==Definition==
Let ''A'' be an object in the concrete category C. Then ''A'' has the ''fixed-point property'' if every morphism (i.e., every function) f:A\to A has a fixed point.
The most common usage is when C=Top is the category of topological spaces. Then a topological space ''X'' has the fixed-point property if every continuous map f:X\to X has a fixed point.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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