Basis elements in the product topology are the entire space in all but finitely many factors. So if infinitely many factor spaces are non-compact, then no basis element is contained in a compact set.
I need help with this exercise..
Let be a collection of topological spaces.
1)prove: If an infinite number of are non-compact, then any compact subset in has empty interior. 2)is there a need for every compact set to be dense nowhere in ( )?
..I look at the product where all are equal to set ) with a topology whose basis consists of sets in form of