On pseudo-compact spaces
On pseudo-compact spaces
On Pseudo-compact Spaces 121 Proof.Let f be an unbounded continuous function on S; put f(x)=arctg(n-lf(x)l). Then {f}No--U.Theorem.If some of the families E, Eo, N, No is contained in U, then S is pseudo-compact.If, conversely, S is pseudo-compact, then U=E=Eo, UN=No.Proof.Lemma 1 implies that NE; now it is obvious thatNo N, …