I'm having trouble with this problem:
Suppose is a paracompact topological space. Let be an open set of which contains . Show that there is a map such that implies .
Note that all my paracompact spaces are assumed to be Hausdorff.
I know that paracompact spaces are in particular normal, and I tried to use an Urysohn function, but I couldn't find one with the right property.
I also attempted a partition of unity, but the codomain of f is not supposed to contain 0, which throws me off.