Hey.

My assignment says the following:

Let $\displaystyle X$ be a topolical space with $\displaystyle \tau $ as its topology. Let $\displaystyle \infty $ be a point not in $\displaystyle X$. Let $\displaystyle X^* = X \cup \{ \infty \} $.

Let $\displaystyle \tau^* = \tau \cup \{ U \in X | X^* \setminus U $ is a closed, compact subset of $\displaystyle X \}$.

(1) Prove that $\displaystyle \tau^*$ is a topology on $\displaystyle X^*$. (I have already done this)

(2) SHow that $\displaystyle (X^* , \tau^* )$ is compact.

I dont know how to show number 2? Could anyone give me a hint or some advice on how to approach this?

Thanks a million.

/Morten