Zvonko Iljazović: Computable topological type

Abstract: A compact subset of Euclidean space is computable if it can be effectively approximated by a finite set of points with rational coordinates with arbitrary precision. A compact subset of Euclidean space is semicomputable if its complement can be effectively covered by rational open balls. Each computable set is semicomputable, but a semicomputable set need not be computable. I will talk about certain topological conditions under which semicomputable sets are computable.