how is a function continuous
In mathematics, a continuous function is, roughly speaking, a function for which small changes in the input result in small changes in the output. Otherwise, a function is said to be a discontinuous function.A continuous function with a continuous inverse function is called a homeomorphism.Continuity of functions is one of the core concepts of topology, which is treated in full generality below.n detail, a function f: X â Y is sequentially continuous if whenever a sequence (x n) in X converges to a limit x, the sequence (f (x n)) converges to f (x). Thus sequentially continuous functions preserve sequential limits.