On the $\cap$-structure spaces

Abstract

The family $\MM_X\sub\mathcal{P}(X)$ is called an $\cap$-structure, when it is closed under the arbitrary intersection. This concept has been studied and considered in algebra, specially in lattices. Using this concept, we define a quasi topological structure which is called $\cap$-structure space. By studying this space, we attempt to explain some  algebraic concepts through this structure.