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
