axioms of separation

Philosophy dictionary. . 2011.

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  • Separation axiom — 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… …   Wikipedia

  • History of the separation axioms — In general topology, the separation axioms have had a convoluted history, with many competing meanings for the same term, and many competing terms for the same concept. Origins Before the current general definition of topological space, there… …   Wikipedia

  • List of axioms — This is a list of axioms as that term is understood in mathematics, by Wikipedia page. In epistemology, the word axiom is understood differently; see axiom and self evidence. Individual axioms are almost always part of a larger axiomatic… …   Wikipedia

  • Peano axioms — In mathematical logic, the Peano axioms, also known as the Dedekind Peano axioms or the Peano postulates, are a set of axioms for the natural numbers presented by the 19th century Italian mathematician Giuseppe Peano. These axioms have been used… …   Wikipedia

  • Axiome de séparation (topologie) —  Ne pas confondre avec le schéma d axiomes de séparation de la théorie des ensembles. En topologie, un axiome de séparation est une propriété satisfaite par certains espaces topologiques, similaire à la propriété de séparation de Hausdorff… …   Wikipédia en Français

  • Axiom schema of predicative separation — In axiomatic set theory, the axiom schema of predicative separation, or of restricted, or Delta;0 separation, is a schema of axioms which is a restriction of the usual axiom schema of separation in Zermelo Fraenkel set theory. It only asserts the …   Wikipedia

  • Kripke–Platek set theory — The Kripke–Platek axioms of set theory (KP) (IPAEng|ˈkrɪpki ˈplɑːtɛk) are a system of axioms of axiomatic set theory, developed by Saul Kripke and Richard Platek. The axiom system is written in first order logic; it has an infinite number of… …   Wikipedia

  • schema — (pl. schemata) In many logical calculi, axioms and rules are presented as forms or schemata, with the provision that any of an infinite number of substitution instances are axioms. For example, the rule of inference modus ponens may be presented… …   Philosophy dictionary

  • Quotient space — In topology and related areas of mathematics, a quotient space (also called an identification space) is, intuitively speaking, the result of identifying or gluing together certain points of a given space. The points to be identified are specified …   Wikipedia

  • Normal space — Separation Axioms in Topological Spaces Kolmogorov (T0) version T0 | T1 | T2 | T2½ | completely T2 T3 | T3½ | T4 | T5 | T6 In topology and related branches of mathematics, a no …   Wikipedia

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