Definition
Let A be a subset of a topological space X. A point x in A is called δ-interior point of A if there is some open neighborhood U such that int(cl(U)) does not meet the complement of A. The set of all interior points of A is called δ-open.
Reference
Raja Mohammad Latif, Topological Properties of δ-Open Sets, King Fahd University of Petroleum & Minerals, Department of Mathematical Sciences, Technical Report Series, TR409 (2009)