= Schauder-Tychonoff fixed-point theorem
{c}
{title2=$T(K)\subseteq K\Longrightarrow\exists x\in K:T(x)=x$}
Every continuous self-map of a nonempty compact convex subset of a <locally convex space> has a <fixed point>. Compactness is in the locally convex topology, which may be weaker than a norm topology. This version permits fixed-point arguments on a <weak-star topology> compact set of <linear functionals>. See https://www.math.purdue.edu/~yipn/543/hartmanODE12-ImpFctFixedPts.pdf[Hartman's fixed-point chapter, Theorem 0.2].
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