sequentially continuous

Let X,Y be topological spacesMathworldPlanetmath. Then a f:XY is said to be sequentially continuous if for every convergent sequence xnx in X, f(xn)f(x) in Y.

Every continuous functionMathworldPlanetmathPlanetmath is sequentially continuous, however the converseMathworldPlanetmath is true only in first-countable spaces (for example in metric spaces).

Title sequentially continuous
Canonical name SequentiallyContinuous
Date of creation 2013-03-22 16:31:17
Last modified on 2013-03-22 16:31:17
Owner ehremo (15714)
Last modified by ehremo (15714)
Numerical id 6
Author ehremo (15714)
Entry type Definition
Classification msc 54C05