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Topic: Theorem of Tychonoff

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	PlanetMath: Tychonoff fixed point theorem
		Notice that a normed vector space is a locally convex topological vector space so this theorem extends the Schauder fixed point theorem.
		"Tychonoff fixed point theorem" is owned by paolini.
		This is version 5 of Tychonoff fixed point theorem, born on 2006-07-07, modified 2007-10-15.
	planetmath.org /encyclopedia/TychonoffFixedPointTheorem.html (129 words)

	Tychonoff's theorem - Wikipedia, the free encyclopedia
		This theorem of Tychonoff has many applications in differential and algebraic topology and in functional analysis, e.g., for the Stone-Čech compactification or in the proof of the Theorem of Banach-Alaoglu.
		Tychonoff's theorem is complex, and its proof is often approached in parts, proving helpful lemmas first.
		To actually prove Tychonoff's theorem, we use the definition of compactness based on the FIP, by taking an FIP collection A of sets, and showing that the intersection over closures of elements of A is nonempty.
	en.wikipedia.org /wiki/Tychonoff's_theorem (1201 words)

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