Changes

A [[differentiable function]] is always continuous, but a continuous function is not always differentiable.

A [[differentiable function]] is always continuous, but a continuous function is not always differentiable.

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]] U in Y, the inverse image of U 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.

A continuous function maps a convergent [[sequence]], [[net]], or [[filter]] to a convergent sequence, net, or filter, respectively.