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Separation Axioms
In topology and related fields of mathematics, there are several restrictions that one often makes on the kinds of topological spaces that one wishes to consider. Some of these restrictions are given by the separation axioms. These are sometimes called ''Tychonoff separation axioms'', after Andrey Tychonoff. The separation axioms are not fundamental axioms like those of Zermelo–Fraenkel set theory, set theory, but rather defining properties which may be specified to distinguish certain types of topological spaces. The separation axioms are denoted with the letter "T" after the German language, German ''Trennungsaxiom'' ("separation axiom"), and increasing numerical subscripts denote stronger and stronger properties. The precise definitions of the history of the separation axioms, separation axioms have varied over time. Especially in older literature, different authors might have different definitions of each condition. Preliminary definitions Before we define the separation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hausdorff Regular Normal Space Diagram
Hausdorff may refer to: People * Felix Hausdorff (1868–1942), German mathematician after whom Hausdorff spaces are named *Natasha Hausdorff (born 1989), British barrister, international news commentator, and Israel advocate Other * A Hausdorff space, when used as an adjective, as in "the real line is Hausdorff" * Hausdorff dimension, a measure theoretic concept of dimension * Hausdorff distance or Hausdorff metric, which measures how far two compact non-empty subsets of a metric space are from each other * Hausdorff density * Hausdorff maximal principle * Hausdorff measure * Hausdorff moment problem * Hausdorff paradox {{disambig, surname ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
