# sequentially continuous

Let $X,Y$ be topological spaces. Then a $f:X\rightarrow Y$ is said to be sequentially continuous if for every convergent sequence $x_{n}\rightarrow x$ in $X$, $f(x_{n})\rightarrow f(x)$ 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 SequentiallyContinuous 2013-03-22 16:31:17 2013-03-22 16:31:17 ehremo (15714) ehremo (15714) 6 ehremo (15714) Definition msc 54C05