dense topology

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• Topology — (Greek topos , place, and logos , study ) is the branch of mathematics that studies the properties of a space that are preserved under continuous deformations. Topology grew out of geometry, but unlike geometry, topology is not concerned with… …   Wikipedia

• Dense set — In topology and related areas of mathematics, a subset A of a topological space X is called dense (in X) if any point x in X belongs to A or is a limit point of A.[1] Informally, for every point in X, the point is either in A or arbitrarily close …   Wikipedia

• Dense submodule — In abstract algebra, specifically in module theory, a dense submodule of a module is a refinement of the notion of an essential submodule. If N is a dense submodule of M, it may also be said it may alternatively be said that N ⊆ M is a… …   Wikipedia

• Dense-in-itself — In mathematics, a subset A of a topological space is said to be dense in itself if A contains no isolated points. Every dense in itself closed set is perfect. Conversely, every perfect set is dense in itself. A simple example of a set which is… …   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

• 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

• 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

• Divisor topology — In mathematics, more specifically general topology, the divisor topology is an example of a topology given to the set X of positive integers that are greater than or equal to two, i.e., X = {2, 3, 4, 5, …}. The divisor topology is the poset… …   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

• 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