Hello,

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 isnotsupposed to contain 0, which throws me off.