Z-半代数格及Z-半Scott拓扑

Z-semialgebraic Lattices and Z-semi Scott Topology

在Z-双小于关系的基础上定义了Z-紧元并依此引入了Z-半代数格及强Z-代数格的概念,证明了一定条件下Z-半代数格的闭包算子的像还是Z-半代数格,强Z-代数格与其Z-紧元集的Z-理想集是同构的。最后,研究了Z-半连续格和Z-半Scott拓扑的基本性质。

The Z-compact elements are defined on the base of Z-way below relation, and the concepts of Z-semialgebraic lattices and strongly Z-algebraic lattices are introduced. It is proved that under certain conditions the image of a closure operator on the Z-semialgebraic lattice is also a Z-semialgebraic lattice, and a strongly Z-algebraic lattice is isomorphic to the set of all Z-ideals of its Z-compact elements. Finally, some properties of Z-semi Scott topology and Z-semieontinuous lattices are studied.