dense-in-itself subset

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• 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 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

• Density (disambiguation) — Density and dense usually refer to a measure of how much of some entity is within a fixed amount of space. Types of density include: In physics, density of mass: Density, mass per volume Area density or surface density, mass over a (two… …   Wikipedia

• Isolated point — 0 is an isolated point of A In topology, a branch of mathematics, a point x of a set S is called an isolated point of S, if there exists a neighborhood of x not containing other points of S. In particular, in a Euclidean space (or in a …   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

• Hilbert space — For the Hilbert space filling curve, see Hilbert curve. Hilbert spaces can be used to study the harmonics of vibrating strings. The mathematical concept of a Hilbert space, named after David Hilbert, generalizes the notion of Euclidean space. It… …   Wikipedia

• 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

• 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

• Rational mapping — In mathematics, in particular the subfield of algebraic geometry, a rational map is a kind of partial function between algebraic varieties. In this article we use the convention that varieties are irreducible.DefinitionA first attemptSuppose we… …   Wikipedia

• Compact space — Compactness redirects here. For the concept in first order logic, see compactness theorem. In mathematics, specifically general topology and metric topology, a compact space is an abstract mathematical space whose topology has the compactness… …   Wikipedia