Hatcher explains on page 5 how a CW complex can be constructed inductively by attaching $n$-cells i.e. open $n$-dimensional disks.
On page 520 in the appendix he writes "A finite CW complex, ... , is compact since attaching a single cell preserves compactness."
Now my question: why is this obvious? An open disk is not compact, so how can I see that sticking two together is?
Many thanks for your help!