# Functional Analysis – Continuous fields of C * algebras of dimension one in a dense set

At a Hausdorff on-site compact space $$X$$Consider a continuous field $${A_x } _ {x in X}$$ by C * -Algebren over $$X$$, so that $$A_x$$ is one-dimensional for everyone $$x$$ in a dense subset $$D$$ from $$X$$while the dimension of $$A_x$$ is greater than one for $$x$$ in the $$X setminus D$$, I can put together some simple examples $$X setminus D$$ is a discrete sentence, but I wonder how much more complicated this can be. I would like to know:

Is it possible to build an example of this? $$D$$ can not be open.