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In mathematics, Tychonoff's theorem states that the product of any collection of compact topological spaces is compact with respect to the product topology...

mathematics, Tychonoff spaces and completely regular spaces are kinds of topological spaces. These conditions are examples of separation axioms. A Tychonoff space...

Tikhonov (Russian: Ти́хонов; masculine), sometimes spelled as Tychonoff, or Tikhonova (Ти́хонова; feminine) is a Russian surname that is derived from...

conjecture for the general case was published in the Scottish book. In 1934, Tychonoff proved the theorem for the case when K is a compact convex subset of a...

spaces are normal; In particular, the Stone–Čech compactification of a Tychonoff space is normal Hausdorff; Generalizing the above examples, all paracompact...

of Tychonoff spaces is Tychonoff. A product of normal spaces need not be normal. Compactness Every product of compact spaces is compact (Tychonoff's theorem)...

defines Tychonoff spaces; or any of the Tychonoff separation axioms. This disambiguation page lists articles associated with the title Tychonoff axiom....

the separation axioms. These are sometimes called Tychonoff separation axioms, after Andrey Tychonoff. The separation axioms are not fundamental axioms...

In mathematics, more specifically in general topology, the Tychonoff cube is the generalization of the unit cube from the product of a finite number of...

method in geophysics. Other transliterations of his surname include "Tychonoff", "Tychonov", "Tihonov", "Tichonov". Born in Gzhatsk, he studied at the...

it is also a Tychonoff space. For this reason, examples of Hausdorff spaces that fail to be locally compact because they are not Tychonoff spaces can be...

In topology, the Tychonoff plank is a topological space defined using ordinal spaces that is a counterexample to several plausible-sounding conjectures...

continuous with a compact image, then f has a fixed point. Tikhonov (Tychonoff) fixed-point theorem: Let V be a locally convex topological vector space...

compact Hausdorff space factors through βX (in a unique way). If X is a Tychonoff space then the map from X to its image in βX is a homeomorphism, so X...

can also show that every regular Hausdorff space is Urysohn and every Tychonoff space (=completely regular Hausdorff space) is completely Hausdorff. In...

versions of these statements are: every locally compact Hausdorff space is Tychonoff, and every compact Hausdorff space is normal Hausdorff. The following...

and {p} are separated by a function. T3½, Tychonoff, Completely regular Hausdorff or Completely T3. A Tychonoff space is a completely regular T0 space....

Since every compact Hausdorff space is a Tychonoff space, and every subspace of a Tychonoff space is Tychonoff, we conclude that any space possessing a...

the Stone–Weierstrass theorem to noncompact Tychonoff spaces, namely, any continuous function on a Tychonoff space is approximated uniformly on compact...

An example of a regular space that is not completely regular is the Tychonoff corkscrew. Most interesting spaces in mathematics that are regular also...