Let $X$ be a topological space.
A subset $U$ of $X$ is sequentially open if each sequence $(x_n)$ in $X$ converging to a point of $U$ is eventually in $U$.
A subset $F$ of $X$ is sequentially closed if, whenever $(x_n)$ is a sequence in $F$ converging to $x$, then $x$ must also be in $F$.
(1):A sequential space is a space $X$ satisfying one of the following equivalent conditions:
Every sequentially open subset of $X$ is open.
Every sequentially closed subset of $X$ is closed.
(2):A KC space is a space that every compact subset is closed.
I have a question:
Is a compact, countable KC-space sequential? Why?