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separable topology

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  • Separable space — In mathematics a topological space is called separable if it contains a countable dense subset; that is, there exists a sequence { x n } {n=1}^{infty} of elements of the space such that every nonempty open subset of the space contains at least… …   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

  • Particular point topology — In mathematics, the particular point topology (or included point topology) is a topology where sets are considered open if they are empty or contain a particular, arbitrarily chosen, point of the topological space. Formally, let X be any set and… …   Wikipedia

  • Long line (topology) — In topology, the long line (or Alexandroff line) is a topological space analogous to the real line, but much longer. Because it behaves locally just like the real line, but has different large scale properties, it serves as one of the basic… …   Wikipedia

  • Weak topology — This article discusses the weak topology on a normed vector space. For the weak topology induced by a family of maps see initial topology. For the weak topology generated by a cover of a space see coherent topology. In mathematics, weak topology… …   Wikipedia

  • Operator topology — In the mathematical field of functional analysis there are several standard topologies which are given to the algebra B(H) of bounded linear operators on a Hilbert space H. Contents 1 Introduction 2 List of topologies on B(H) 3 …   Wikipedia

  • Lower limit topology — In mathematics, the lower limit topology or right half open interval topology is a topology defined on the set R of real numbers; it is different from the standard topology on R and has a number of interesting properties. It is the topology… …   Wikipedia

  • Order topology — In mathematics, an order topology is a certain topology that can be defined on any totally ordered set. It is a natural generalization of the topology of the real numbers to arbitrary totally ordered sets. If X is a totally ordered set, the order …   Wikipedia

  • List of general topology topics — This is a list of general topology topics, by Wikipedia page. Contents 1 Basic concepts 2 Limits 3 Topological properties 3.1 Compactness and countability …   Wikipedia

  • Ultrastrong topology — In functional analysis, the ultrastrong topology, or sigma; strong topology, or strongest topology on the set B(H) of bounded operators on a Hilbert space is the topology defined by the family of seminorms pw(x) for positive elements w of the… …   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

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