Let U be an open bounded subset of R^n, and K a compact subset of U. Does there always exist a compact subset L of U that contains K, and such that L is a retract of U.
Looks to me true as I can get as close as I wish with L to the to the limit boundary of U and contain any compact K. As L is close enough it will
have all the connectivity properties of U and will be a retract...but how do I prove it?