Thread: Sub bases

Can anybody help me with this questions:
Let (X,T) be T1 space. Show that there is 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

Originally Posted by Turloughmack

Can anybody help me with this questions:
Let (X,T) be T1 space. Show that there is 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

I have yet to see you put any effort forward towards these solutions. Care to give us some work?