Abstract
Various concepts related to (L, circle dot)- smooth topological spaces have been established, and relations among them studied by several authors (Kim, Abdel-Sattar, etc.). In this articale, we study the notions of three sorts of neighborhood structures of (L, circle dot)- smooth topological spaces and give some of their properties which are results by Ying [19] extended to (L, circle dot)- smooth topological spaces