sequentially continuous

Let $X,Y$ be topological spaces. Then a $f:X\to Y$ is said to be sequentially continuous if for every convergent sequence $x_n\to x$ in $X$, $f(x_n)\to f(x)$ in $Y$.

Every continuous function is sequentially continuous, however the converse 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