Hausdorff L-topological spaces over a base space

摘要

In this paper, we introduce the notion of Hausdorff L-topological spaces over a base space, where L is a complete lattice and give some characterizations of these spaces. And we show that the category of Hausdorff L-topological spaces over a base space is a reflective subcategory of the category of L-topological spaces over a base space.