I'd like to know if I'm expressing this correctly. Apologies in advance: topology and I have never been well acquainted.
Let $(m,\mathcal B, X)$ be a measure space, and $\mathcal H \subset \mathcal B$ is a sub-$\sigma$-algebra. Suppose we have a $\mathcal B$ measurable function $f$ equal to it's conditional expectation $$ f(x) = E_m(f \, | \mathcal H)(x). $$
What I want to say is that if $a,b\in X$ are separable under $\mathcal B$ (i.e. belong to different open sets) but not under $\mathcal H$ then $$f(a) = f(b).$$ How would a topologist express this?