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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 function from U to a discrete uniform space is constant. A uniform space U is called uniformly disconnected if it is not uniformly connected.
Thus, when discussing simply connected topological spaces, it is far more common to speak of simple connectivity than simple connectedness. On the other hand, in fields without a formally defined notion of connectivity, the word may be used as a synonym for connectedness. Another example of connectivity can be found in regular tilings.
In mathematics, the Fulton–Hansen connectedness theorem is a result from intersection theory in algebraic geometry, for the case of subvarieties of projective space with codimension large enough to make the intersection have components of dimension at least 1.
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Print/export Download as PDF; Printable version; In other projects ... In mathematics, the connectedness theorem may be one of Deligne's connectedness theorem ...
Connectedness defines a fairly general class of commutative rings. For example, all local rings and all (meet-)irreducible rings are connected. In particular, all integral domains are connected. Non-examples are given by product rings such as Z × Z; here the element (1, 0) is a non-trivial idempotent.
In mathematics, Grothendieck's connectedness theorem, [1] [2] states that if A is a complete Noetherian local ring whose spectrum is k-connected and f is in the maximal ideal, then Spec(A/fA) is (k − 1)-connected.
The percolation threshold is a mathematical concept in percolation theory that describes the formation of long-range connectivity in random systems. Below the threshold a giant connected component does not exist; while above it, there exists a giant component of the order of system size.