The topology for $X\bigcup \{\infty\}$ is defined as follows: there are two kinds of open sets of $X\bigcup \{\infty\}$ If $\infty \notin U$ then $U$ is open if and only if $U$ is an open set in the topology of $X$ If $\infty \in U$ then $U$ is open if and only if $U$ is the complement of a closed compact subset $K$ of $X$