/sci/ - Science & Math

Any ideas on where to go from here? I know I need to construct some neighborhood of [math]\{A\}[/math] in the quotient space that doesn't contain any of the [math]U_n[/math]s but I can't see how to make one from the original space.

Pic related is what I have so far, just the set-up.

I know I need to find an open set in the quotient [math]X/A[/math] that contains the point [math]\{A\}[/math] but does not contain any of the [math]U_n[/math].

I know it has something to do with the [math]V_n[/math] in the original space but I don't know how to obtain the needed set.