haʊˈɛvɚɹ ɪts klˈoʊʒɚ ðə klˈoʊʒɚɹ əvə kəmpˈækt sˈɛt ɪz ðɪ ɛntˈaɪɚ spˈeɪs ˈɛks, ænd ɪf ˈɛks ɪz ˈɪnfɪnət ðɪs ɪz nˌɑːt kəmpˈækt.
However its closure (the closure of a compact set) is the entire space X, and if X is infinite this is not compact.