 |
|
| |
|
|
|
at Global Oneness Community.
Share your dreams and let others help you with the interpretation!
Dream Sharing Forum
|
|
Tychonoff space - Definitions | | Tychonoff space - Definitions: Encyclopedia II - Tychonoff space - Definitions | | Suppose 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 | | | Tychonoff space, Tychonoff space - Definitions, Tychonoff space - Examples and counterexamples, Tychonoff space - Properties | | |
| | | Tychonoff space: Encyclopedia II - Tychonoff space - Definitions
Tychonoff space - Definitions
Suppose 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 if it is both completely regular and Hausdorff).
Completely regular spaces and Tychonoff spaces are related through the notion of Kolmogorov equivalence. A topological space is Tychonoff iff it's both completely regular and T0. On the other hand, a space is completely regular iff its Kolmogorov quotient is Tychonoff.
Other related archives0, 1, Andrey Nikolayevich Tychonoff, CW complex, Euclidean topology, Hausdorff, Kolmogorov equivalence, Kolmogorov quotient, Russian, Separation axioms, Stone-Cech compactification, T0, Topology, closed set, compact, compactifications, completion, composition, continuous function, dense, embedded, given any, iff, initial topologies, injective, inverse, locally compact, mathematical analysis, mathematics, metric space, normal, order topology, point, product spaces, pseudometric space, real line, regular, separated by a function, separation axioms, subspaces, there is, topological group, topological manifold, topological spaces, topology, totally ordered set, uniform space, uniform structure, unique, universal property
 Adapted from the Wikipedia article "Definitions", under the G.N U Free Docmentation License. Please also see http://en.wikipedia.org/wiki |
|
|
|
More material related to Tychonoff Space can be found here:
|
|
|
« Back
|
Search the Global Oneness web site |
|
|
|
|
|
Sneak-Peek of Global Oneness Community
Hi friend! The Global Oneness Community, the place for information and sharing about Oneness is not really launched yet (you will see there is still some clean up to do) ...but it is now open for a sneak-peek! And if you wish - please register and become one of the very first members to do so! Jonas
Forum Home,
Articles,
Photo Gallery,
Videos,
News,
Sitemap
...and much more!
|
