Can anybody help me with this questions:

Let (X,T) be T1 space. Show that there is http://www.mathhelpforum.com/math-he...225f6785ab.png space iff there is a subbase S for T such that:

x ε H εS implies that there exists a continuous f:x->[0,1] such that f(x) = 1 and f(y) =0 for all y ε X-H