# Connected Components

### Some articles on connected components, component, connected, components:

Lorentz Group - Connected Components
... As a manifold, it has four connected components ... The identity component of the Lorentz group is the set of all Lorentz transformations preserving both orientation and the direction of time ... isomorphic copy of the Klein four-group label the four connected components of the Lorentz group ...
Stallings Theorem About Ends Of Groups - Ends of Graphs
... Let Γ be a connected graph where the degree of every vertex is finite ... of Γ the graph Γ − F has at most n infinite connected components ... Informally, e(Γ) is the number of "connected components at infinity" of Γ ...
Clopen Set - Properties
... A topological space X is connected if and only if the only clopen sets are the empty set and X ... Any clopen set is a union of (possibly infinitely many) connected components ... If all connected components of X are open (for instance, if X has only finitely many components, or if X is locally connected), then a set is clopen in X if and only ...
Locally Connected Space - Components and Path Components
... Then, if each is connected (respectively, path connected) then the union is connected (respectively, path connected) ... if there is a connected subset of X containing both x and y and if there is a path connected subset of X containing both x and y ... Moreover, if x and y are contained in a connected (respectively, path connected) subset A and y and z are connected in a connected (respectively, path connected) subset B, then the Lemma ...

### Famous quotes containing the words components and/or connected:

Hence, a generative grammar must be a system of rules that can iterate to generate an indefinitely large number of structures. This system of rules can be analyzed into the three major components of a generative grammar: the syntactic, phonological, and semantic components.
Noam Chomsky (b. 1928)

When, in the course of human events, it becomes necessary for one people to dissolve the political bands which have connected them with another, and to assume the powers of the earth, the separate and equal station to which the laws of nature and of nature’s God entitle them, a decent respect to the opinions of mankind requires that they should declare the causes which impel them to the separation.
Thomas Jefferson (1743–1826)