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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.
In mathematics compact convergence (or uniform convergence on compact sets) is a type of convergence that generalizes the idea of uniform convergence. It is associated with the compact-open topology .
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.
Since du is non-zero and the square of the Hodge star operator is −1 on 1-forms, du and dv must be linearly independent, so that u and v give local isothermal coordinates. The existence of isothermal coordinates can be proved by other methods, for example using the general theory of the Beltrami equation , as in Ahlfors (2006) , or by direct ...
In mathematics, a topological space (X, T) is called completely uniformizable [1] (or Dieudonné complete [2]) if there exists at least one complete uniformity that induces the topology T.
The unit sphere can be replaced with the closed unit ball in the definition. Namely, a normed vector space is uniformly convex if and only if for every < there is some > so that, for any two vectors and in the closed unit ball (i.e. ‖ ‖ and ‖ ‖) with ‖ ‖, one has ‖ + ‖ (note that, given , the corresponding value of could be smaller than the one provided by the original weaker ...
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.
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.