Abstract The study of the sobriety Scott spaces has got a relatively long history in domain theory. Lawson and Hoffmann independently proved that space every continuous directed complete poset (usually called domain) is sober. Johnstone constructed first whose non-sober. Soon after, Isbell gave lattice with non-sober space. Based on Isbell’s example, Xu, Xi, Zhao showed there even Heyting algeb...

This paper studies rough approximation via join and meet on a complete orthomodular lattice. Different from Boolean algebra, the distributive law of over does not hold in lattices. Some properties rely law. Furthermore, we study relationship among law, lattice-valued relation.

An empty simplex is a lattice with only its vertices as points. Their classification in dimension three was completed by White 1964. In four, the same task started 1988 Mori, Morrison, and their motivation coming from close relationship between simplices terminal quotient singularities. They conjectured of prime volume, modulo finitely many exceptions. conjecture proved Sankaran (1990) simplifi...

In this paper, at first we define the concepts of response function and accessible states of a complete residuated lattice-valued (for simplicity we write $mathcal{L}$-valued) tree automaton with a threshold $c.$ Then, related to these concepts, we prove some lemmas and theorems that are applied in considering some decision problems such as finiteness-value and emptiness-value of recognizable t...