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

Hausdorff. Every product of regular spaces is regular. Every product of Tychonoff spaces is Tychonoff. A product of normal spaces need not be normal. Compactness...

they are not Tychonoff spaces can be found in the article dedicated to Tychonoff spaces. But there are also examples of Tychonoff spaces that fail to...

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

Hausdorff; All compact Hausdorff spaces are normal; In particular, the Stone–Čech compactification of a Tychonoff space is normal Hausdorff; Generalizing...

topological spaces that one wishes to consider. Some of these restrictions are given by the separation axioms. These are sometimes called Tychonoff separation...

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...

Kolmogorov space X {\displaystyle X} is a Hausdorff space X {\displaystyle X} is a Tychonoff space for any compatible uniform structure, the intersection...

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

subspace of a Tychonoff space is Tychonoff, we conclude that any space possessing a Hausdorff compactification must be a Tychonoff space. In fact, the...

statements are: every locally compact Hausdorff space is Tychonoff, and every compact Hausdorff space is normal Hausdorff. The following results are some...

is a compact convex subset of a locally convex space. This version is known as the Schauder–Tychonoff fixed-point theorem. B. V. Singbal proved the theorem...

Hausdorff spaces, unlike the Stone–Čech compactification which exists for any topological space (but provides an embedding exactly for Tychonoff spaces). A...

proved in 1926, and the Tychonoff's theorem, which states that every product of arbitrarily many compact topological spaces is again compact. In his...

Every Tychonoff space is embeddable into a product space of the closed unit intervals [ 0 , 1 ] . {\displaystyle [0,1].} Actually, every Tychonoff space that...

on a compact Hausdorff space. Further, there is a generalization of the Stone–Weierstrass theorem to noncompact Tychonoff spaces, namely, any continuous...

paracompact spaces may not be paracompact. Compare this to Tychonoff's theorem, which states that the product of any collection of compact topological spaces is...

entire space X. Tychonoff A Tychonoff space (or completely regular Hausdorff space, completely T3 space, T3.5 space) is a completely regular T0 space. (A...

unit intervals. The Tychonoff cube is named after Andrey Tychonoff, who first considered the arbitrary product of topological spaces and who proved in the...

definition of pseudocompactness. Pseudocompact spaces were defined by Edwin Hewitt in 1948. For a Tychonoff space X to be pseudocompact requires that every...

space is also called an accessible space or a space with Fréchet topology and an R0 space is also called a symmetric space. (The term Fréchet space also...

covering dimension can be extended from the class of normal spaces to all Tychonoff spaces merely by replacing the term "open" in the definition by the...

example, they are Hausdorff paracompact spaces (and hence normal and Tychonoff) and first-countable. However, some properties of the metric, such as...

convex subset of a Banach space V. If f : C → C is continuous with a compact image, then f has a fixed point. Tikhonov (Tychonoff) fixed-point theorem: Let...

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

topology and related branches of mathematics, a topological space X is a T0 space or Kolmogorov space (named after Andrey Kolmogorov) if for every pair of distinct...

regular Hausdorff or Completely T3. A Tychonoff space is a completely regular T0 space. (A completely regular space is Hausdorff if and only if it is T0...

space T1 space Hausdorff space Completely Hausdorff space Regular space Tychonoff space Normal space Urysohn's lemma Tietze extension theorem Paracompact...

Banach–Alaoglu theorem can be proved using Tychonoff's theorem about infinite products of compact Hausdorff spaces. When X {\displaystyle X} is separable...

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