Separation Axioms

  • To Space

    A topological space is said to be a space if for any pair of distinct points of , there exist at least one open set which contains one of them but not the other. In other words, a topological space is said to be a space if for any , there exist an open set […]

  • T1 Space

    A topological space is said to be a space if for any pair of distinct points of , there exist two open sets which contain one but not the other. In other words, a topological space is said to be a space if for any there exist open sets and such that and . Example: […]

  • T2 Space or Hausdorff Space

    A Hausdorff space is a topological space in which each pair of distinct points can be separated by disjoint open set. In other words, a topological space is said to be a space or Hausdorff space if for any , there exist open sets and such that and . Example: Let be a non-empty set […]

  • Completely Regular Space

    A topological space is said to be completely regular space, if every closed set in and a point , , then there exist a continuous function , such that and . In other words, a topological space is said to be a completely regular space if for any and a closed set not containing , […]

  • Regular Space

    Let be a topological space, then for every non-empty closed set and a point which does not belongs to , there exist open sets and , such that and . In other words, a topological space is said to be a regular space if for any and any closed set of , there exist an […]

  • Normal Space

    Let be a topological space and, and are disjoint closed subsets of , then is said to be normal space, if there exist open sets and such that , . In other words, a topological space is said to be a normal space if for any disjoint pair of closed sets and , there exist […]