Exercise 17, § 4

Now prove that every Weierstrass normal space $X$ (IX, p. 88, exerc. 20) is semi-compact (IX, p. 93, exerc. 13). (Prove that if $(x_n)$ is a sequence of points of $X$ admitting no adherence value, there is a numerical function $f$ finite and continuous in $X$ such that $f(x_n) = n$ for every $n$.)