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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 .
A topological space is said to be connected if it is not the union of two disjoint nonempty open sets. [2] A set is open if it contains no point lying on its boundary; thus, in an informal, intuitive sense, the fact that a space can be partitioned into disjoint open sets suggests that the boundary between the two sets is not part of the space, and thus splits it into two separate pieces.
Every Riemann surface is the quotient of the free, proper and holomorphic action of a discrete group on its universal covering and this universal covering, being a simply connected Riemann surface, is holomorphically isomorphic (one also says: "conformally equivalent" or "biholomorphic") to one of the following: the Riemann sphere; the complex ...
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.
A topological space X is path-connected if and only if its 0th homotopy group vanishes identically, as path-connectedness implies that any two points x 1 and x 2 in X can be connected with a continuous path which starts in x 1 and ends in x 2, which is equivalent to the assertion that every mapping from S 0 (a discrete set of two points) to X ...
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.
Print/export Download as PDF; Printable version; In other projects ... In mathematics, the connectedness theorem may be one of Deligne's connectedness theorem ...