dense set

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• 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

• Nowhere dense set — A subset A of a topological space X is nowhere dense in X if and only if the interior of the closure of A is empty. The order of operations is important. For example, the set of rational numbers, as a subset of R has the property that the closure …   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

• Dense order — In mathematics, a partial order ≤ on a set X is said to be dense if, for all x and y in X for which x < y, there is a z in X such that x < z < y. The rational numbers with the ordinary ordering are a densely ordered set in this sense, as …   Wikipedia

• Set (mathematics) — This article gives an introduction to what mathematicians call intuitive or naive set theory; for a more detailed account see Naive set theory. For a rigorous modern axiomatic treatment of sets, see Set theory. The intersection of two sets is… …   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 — adjective (denser; densest) Etymology: Latin densus; akin to Greek dasys thick with hair or leaves Date: 15th century 1. a. marked by compactness or crowding together of parts < dense vegetation > < dense traffic > …   New Collegiate Dictionary

• dense — adjective 1) a dense forest Syn: thick, close packed, tightly packed, closely set, close set, crowded, crammed, compact, solid, tight; overgrown, jungly, impenetrable, impassable Ant …   Thesaurus of popular words

• dense — /dɛns / (say dens) adjective (denser, densest) 1. having the component parts closely compacted together; compact: a dense forest; dense population. 2. thickheaded; obtuse; stupid. 3. intense: dense ignorance. 4. Photography (of a developed… …  

• Meagre set — In the mathematical fields of general topology and descriptive set theory, a meagre set (also called a meager set or a set of first category) is a set that, considered as a subset of a (usually larger) topological space, is in a precise sense… …   Wikipedia

• List of exceptional set concepts — This is a list of exceptional set concepts. In mathematics, and in particular in mathematical analysis, it is very useful to be able to characterise subsets of a given set X as small , in some definite sense, or large if their complement in X is… …   Wikipedia