# A polar open set in a topological subspace?

Suppose $$U$$ is a bounded open set in $$\mathbb{R}^m$$ with ($$m\geq2$$). Is it possible to have a non-empty set $$E$$ in the boundary $$\partial U$$ of $$U$$ that is open in $$\partial U$$ and is polar? A set $$E$$ is called polar if there exists a superharmonic function on an open neighborhood of $$E$$ that takes the value of $$\infty$$ at each point of $$E$$.

• What do you mean by a polar set? Jun 21, 2021 at 3:03
• Sorry! I added the definition. Jun 21, 2021 at 4:18