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  • Trivial topology — In topology, a topological space with the trivial topology is one where the only open sets are the empty set and the entire space. Such a space is sometimes called an indiscrete space, and its topology sometimes called an indiscrete topology.… …   Wikipedia

  • Glossary of topology — This is a glossary of some terms used in the branch of mathematics known as topology. Although there is no absolute distinction between different areas of topology, the focus here is on general topology. The following definitions are also… …   Wikipedia

  • Finite topological space — In mathematics, a finite topological space is a topological space for which the underlying point set is finite. That is, it is a topological space for which there are only finitely many points.While topology is mostly interesting only for… …   Wikipedia

  • Uniform space — In the mathematical field of topology, a uniform space is a set with a uniform structure. Uniform spaces are topological spaces with additional structure which is used to define uniform properties such as completeness, uniform continuity and… …   Wikipedia

  • Kolmogorov space — In topology and related branches of mathematics, the T0 spaces or Kolmogorov spaces, named after Andrey Kolmogorov, form a broad class of well behaved topological spaces.The T0 condition is one of the separation axioms. Definition A T0 space is a …   Wikipedia

  • Locally convex topological vector space — In functional analysis and related areas of mathematics, locally convex topological vector spaces or locally convex spaces are examples of topological vector spaces (TVS) which generalize normed spaces. They can be defined as topological vector… …   Wikipedia

  • Topological indistinguishability — In topology, two points of a topological space X are topologically indistinguishable if they have exactly the same neighborhoods. That is, if x and y are points in X, and A is the set of all neighborhoods which contain x, and B is the set of all… …   Wikipedia

  • Partition topology — In mathematics, the partition topology is a topology that can be induced on any set X by partitioning X into disjoint subsets P; these subsets form the basis for the topology. There are two important examples which have their own names: The… …   Wikipedia

  • Normed vector space — In mathematics, with 2 or 3 dimensional vectors with real valued entries, the idea of the length of a vector is intuitive and can easily be extended to any real vector space Rn. The following properties of vector length are crucial. 1. The zero… …   Wikipedia

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