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A function f: X -> Y mapping elements in a [[topological space]] X to a topological space Y is continuous if for every [[open set]] in Y, the inverse image of Y under f is an open subset of X.
A function f: X -> Y mapping elements in a [[topological space]] X to a topological space Y is continuous if for every [[open set]] in Y, the inverse image of Y under f is an open subset of X.
A continuous function maps a convergent [[sequence]], [[net]], or [[filter]] to a convergent sequence, net, or filter, respectively.
[[category: mathematics]]
[[category: mathematics]]