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indiscrete space

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  • Discrete space — In topology, a discrete space is a particularly simple example of a topological space or similar structure, one in which the points are isolated from each other in a certain sense. Contents 1 Definitions 2 Properties 3 Uses …   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

  • Regular space — In topology and related fields of mathematics, regular spaces and T3 spaces are particularly convenient kinds of topological spaces.Both conditions are examples of separation axioms. Definitions Suppose that X is a topological space. X is a… …   Wikipedia

  • Approach space — In topology, approach spaces are a generalization of metric spaces, based on point to set distances, instead of point to point distances. They were introduced by [http://www.math.ua.ac.be/TOP/ Robert Lowen] in 1989.DefinitionGiven a metric space… …   Wikipedia

  • Topological space — Topological spaces are mathematical structures that allow the formal definition of concepts such as convergence, connectedness, and continuity. They appear in virtually every branch of modern mathematics and are a central unifying notion. The… …   Wikipedia

  • Perfect space — In mathematics, in the field of topology, perfect spaces are spaces that have no isolated points. In such spaces, every point can be approximated arbitrarily well by other points given any point and any topological neighborhood of the point,… …   Wikipedia

  • Toronto space — In mathematics, in the realm of topology, a Toronto space is a topological space that is homeomorphic to every proper subspace of the same cardinality.There are five homeomorphism classes of countable Toronto spaces, namely: the discrete topology …   Wikipedia

  • 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

  • Closure (topology) — For other uses, see Closure (disambiguation). In mathematics, the closure of a subset S in a topological space consists of all points in S plus the limit points of S. Intuitively, these are all the points that are near S. A point which is in the… …   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

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