View source for Continuity

One of the most important mathematical concepts, as a rule used in connection with the concept of a mapping (see [[Continuous function|Continuous function]]; [[Continuous mapping|Continuous mapping]]; [[Continuous operator|Continuous operator]]). In particular, one can study the continuity of a certain algebraic operation in a given set relative to a topology on that set. When the operation in question is continuous, the term  "continuity"  is also applied to the set itself (for example, [[Continuous group|continuous group]]). The term  "continuity"  is also used in the sense that it is impossible to  "complete by continuity"  a certain mathematical object and thus (non-trivially) extend it, for example, a metric space; in this sense one speaks of the continuity of the set of real numbers.