Construction and Spectral Topology on Hyperlattices

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}}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 úx = {x}{x vee x = {x}} for all x ? L{x in L} and there exist x, y ? L{x, y in L} which card(x úy) 1 1{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 S(L){{{mathcal S}(L)}}, then we show that S(L){{{mathcal S}(L)}} is a T ₀-space. At the end, we obtain that each complemented distributive hyperlattice is a T ₁-space.