totally disconnected space

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• Totally disconnected space — In topology and related branches of mathematics, a totally disconnected space is a topological space which is maximally disconnected, in the sense that it has no non trivial connected subsets. In every topological space the empty set and the one… …   Wikipedia

• Extremally disconnected space — In mathematics, a topological space is termed extremally disconnected or extremely disconnected if the closure of every open set in it is open. (The term extremally disconnected is usual, even though the word extremally does not appear in most… …   Wikipedia

• Locally connected space — In this topological space, V is a neighbourhood of p and it contains a connected neighbourhood (the dark green disk) that contains p. In topology and other branches of mathematics, a topological space X is locally connected if every point admits… …   Wikipedia

• T1 space — In topology and related branches of mathematics, T1 spaces and R0 spaces are particular kinds of topological spaces.The T1 and R0 properties are examples of separation axioms. Definitions Let X be a topological space and let x and y be points in… …   Wikipedia

• Connected space — For other uses, see Connection (disambiguation). Connected and disconnected subspaces of R² The green space A at top is simply connected whereas the blue space B below is not connected …   Wikipedia

• Perfect space — In mathematics, in the field of topology, perfect spaces are spaces that have no isolated points. In such spaces, every point can be approximated arbitrarily well by other points given any point and any topological neighborhood of the point,… …   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

• Zero-dimensional space — In mathematics, a topological space is zero dimensional or 0 dimensional, if its topological dimension is zero, or equivalently, if it has a base consisting of clopen sets. A zero dimensional Hausdorff space is necessarily totally disconnected,… …   Wikipedia

• Discrete two-point space — In topology, a branch of mathematics, a discrete two point space is the simplest example of a totally disconnected discrete space. The points can be denoted by the symbols 0 and 1. Any disconnected space has a continuous mapping onto the… …   Wikipedia

• Discrete space — In topology, a discrete space is a particularly simple example of a topological space or similar structure, one in which the points are isolated from each other in a certain sense. Contents 1 Definitions 2 Properties 3 Uses …   Wikipedia

• Cantor space — In mathematics, the term Cantor space is sometimes used to denotethe topological abstraction of the classical Cantor set:A topological space is aCantor space if it is homeomorphic to the Cantor set.The Cantor set itself is of course a Cantor… …   Wikipedia