Tychonoff fixed point theorem

Let X be a locally convex topological vector space, and let KX be a non-empty, compactPlanetmathPlanetmath, and convex set. Then given any continuous mapping f:KK there exists xK such that f(x)=x.

Notice that a normed vector spacePlanetmathPlanetmath is a locally convex topological vector space so this theorem extends the Schauder fixed point theoremMathworldPlanetmath.


Title Tychonoff fixed point theorem
Canonical name TychonoffFixedPointTheorem
Date of creation 2013-03-22 16:04:11
Last modified on 2013-03-22 16:04:11
Owner paolini (1187)
Last modified by paolini (1187)
Numerical id 8
Author paolini (1187)
Entry type Theorem
Classification msc 54H25
Classification msc 46B50
Classification msc 47H10
Related topic SchauderFixedPointTheorem
Related topic BrouwerFixedPointTheorem