connected complement

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• 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

• simply-connected — /sim plee keuh nek tid/, adj. Math. 1. (of a set or domain) having a connected complement. 2. (of a set or domain) having the property that every simple closed curve in the set can be shrunk to a point without intersecting the boundary of the set …   Universalium

• simply-connected — /sim plee keuh nek tid/, adj. Math. 1. (of a set or domain) having a connected complement. 2. (of a set or domain) having the property that every simple closed curve in the set can be shrunk to a point without intersecting the boundary of the set …   Useful english dictionary

• 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

• 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

• Strongly connected component — Graph with strongly connected components marked A directed graph is called strongly connected if there is a path from each vertex in the graph to every other vertex. In particular, this means paths in each direction; a path from a to b and also a …   Wikipedia

• Surface of class VII — In mathematics, surfaces of class VII are non algebraic complex surfaces studied by (Kodaira 1964, 1968) that have Kodaira dimension −∞ and first Betti number 1. Minimal surfaces of class VII (those with no rational curves with self… …   Wikipedia

• HEBREW GRAMMAR — The following entry is divided into two sections: an Introduction for the non specialist and (II) a detailed survey. [i] HEBREW GRAMMAR: AN INTRODUCTION There are four main phases in the history of the Hebrew language: the biblical or classical,… …   Encyclopedia of Judaism

• 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

• Modular decomposition — In graph theory, the modular decomposition is a decomposition of an undirected graph into subsets of vertices called modules. A module is a generalization of a connected component of a graph. Unlike connected components, however, one module can… …   Wikipedia

• Claw-free graph — A claw In graph theory, an area of mathematics, a claw free graph is a graph that does not have a claw as an induced subgraph. A claw is another name for the complete bipartite graph K1,3 (that is, a star graph with three edges, three leaves, and …   Wikipedia