 Tychonoff space - Examples and counterexamples: Encyclopedia II - Tychonoff space - DefinitionsSuppose that X is a topological space.
X is a completely regular space iff, given any closed set F and any point x that does not belong to F, there is a continuous function f from X to the real line R such that f(x) is 0 and f(y) is 1 for every y in F. In fancier terms, this condition says that x and F can be separated by a function.
X is a Tychonoff space, or T3½ space, or Tπ space, or completely T3 space if and only i ...
See also:Tychonoff space, Tychonoff space - Definitions, Tychonoff space - Examples and counterexamples, Tychonoff space - Properties Read more here: » Tychonoff space: Encyclopedia II - Tychonoff space - Definitions |
