Construction and Spectral Topology on Hyperlattices

Abstract

In this paper by considering the notion of hyperlattice, we introduce good and s-good hyperlattices, homomorphism of hyperlattices and s-reflexives. We give some examples of them and we study their structures. We show that there exists a hyperlattice L such that ${x \vee x = \{x\}}$ for all ${x \in L}$ and there exist ${x, y \in L}$ which ${card(x \vee y) \ne 1}$. Also, we define a topology on the set of prime ideals of a distributive hyperlattice L and we will call it ${{{\mathcal S}(L)}}$, then we show that ${{{\mathcal S}(L)}}$ is a T ₀-space. At the end, we obtain that each complemented distributive hyperlattice is a T ₁-space.