# connected space

connected space
Any topological space which cannot be written as the disjoint union of two or more nonempty open spaces

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• 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

• Connected space/Proofs — Every path connected space is connectedLet S be path connected and suppose, for contradiction, that S is not connected. Then S = A cup B for nonempty disjoint open sets A and B . Let x in A, y in B. Since S is path connected, there exists a… …   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

• Simply connected space — In topology, a topological space is called simply connected (or 1 connected) if it is path connected and every path between two points can be continuously transformed, staying within the space, into any other path while preserving the two… …   Wikipedia

• N-connected space — n connected redirects here; for the concept in graph theory see Connectivity (graph theory). In the mathematical branch of topology, a topological space X is said to be n connected if and only if it is path connected and its first n homotopy… …   Wikipedia

• Locally simply connected space — In mathematics, a locally simply connected space is a topological space that admits a basis of simply connected sets. Every locally simply connected space is also locally path connected and locally connected.The circle is an example of a locally… …   Wikipedia

• Uniformly connected space — In topology and related areas of mathematics a uniformly connected space or Cantor connected space is a uniform space U such that every uniformly continuous functions from U to a discrete uniform space is constant.A uniform space U is called… …   Wikipedia

• space — 1. noun /speɪs/ a) The intervening contents of a volume. If it be only a Single Letter or two that drops, he thruſts the end of his Bodkin between every Letter of that Word, till he comes to a Space: and then perhaps by forcing thoſe Letters… …   Wiktionary

• Connected ring — In mathematics, especially in the field of commutative algebra, a connected ring is a commutative ring A that satisfies one of the following equivalent conditions: A possesses no non trivial (that is, not equal to 1 or 0) idempotent elements; the …   Wikipedia

• Connected-component labeling — (alternatively connected component analysis, blob extraction, region labeling, blob discovery, or region extraction) is an algorithmic application of graph theory, where subsets of connected components are uniquely labeled based on a given… …   Wikipedia