This paper studies a sort of topological spaces by introducing ψ—factor, and discusses the subspace and product spaces of the sort of topological spaces by using Galois theory.
本文第一部分利用完备格上的上拓扑子基,给出完全分配格与点格的若干新刻划,并讨论其上的 Scott 拓扑与 Lawson 拓扑的基与子基的构造.第二部分讨论点格与代数格的关系,证明了 L 是点格当且仅当 L 为代数格且 L^(op)为完全 Heyting代数...本文第一部分利用完备格上的上拓扑子基,给出完全分配格与点格的若干新刻划,并讨论其上的 Scott 拓扑与 Lawson 拓扑的基与子基的构造.第二部分讨论点格与代数格的关系,证明了 L 是点格当且仅当 L 为代数格且 L^(op)为完全 Heyting代数,并证明了代数偏序集范畴与点格范畴是等价的.展开更多
Let L be a complete lattice and x, y ∈ L. We write x y iff for any subset X of L the relation y≤supX always implies the existence of an x~* ∈ X with x≤x~*. Define ↓x={y ∈L:y x} and ↑x ={y ∈L: x y}. If x x, the...Let L be a complete lattice and x, y ∈ L. We write x y iff for any subset X of L the relation y≤supX always implies the existence of an x~* ∈ X with x≤x~*. Define ↓x={y ∈L:y x} and ↑x ={y ∈L: x y}. If x x, then x is called a completely co-prime of L. The set of all completely co-primes of L is denoted by PO(L). L is called a point lattice展开更多
文摘This paper studies a sort of topological spaces by introducing ψ—factor, and discusses the subspace and product spaces of the sort of topological spaces by using Galois theory.
文摘本文第一部分利用完备格上的上拓扑子基,给出完全分配格与点格的若干新刻划,并讨论其上的 Scott 拓扑与 Lawson 拓扑的基与子基的构造.第二部分讨论点格与代数格的关系,证明了 L 是点格当且仅当 L 为代数格且 L^(op)为完全 Heyting代数,并证明了代数偏序集范畴与点格范畴是等价的.
文摘Let L be a complete lattice and x, y ∈ L. We write x y iff for any subset X of L the relation y≤supX always implies the existence of an x~* ∈ X with x≤x~*. Define ↓x={y ∈L:y x} and ↑x ={y ∈L: x y}. If x x, then x is called a completely co-prime of L. The set of all completely co-primes of L is denoted by PO(L). L is called a point lattice
