Co-compact Element In Locale And Co-compact Generate Locale

Since the open set (or neighborhood) as a research abstract space the basic concept of the continuity, The topological space is seen as a some open sets by a lattice structure of the object.After topology and the contact between the lattice theory drew the attention of people. Using the lattice theory method and technique of the characteristic of topology, Thus drawn about the topology of the conclusion with universal meaning.Frame theory or Locale theory, as a new subject has caused the attention of people, and in the mathematical logic, computer science, category theory, topology, algebra, etc also widely used.This paper mainly studies the Locale more than more than tight yuan and generate Locale, the more tight yuan for the first and second countability countability, put forward the first count more than in tight before, are given a separation of the concept of grain, construct a DiJiang column, and discusses the tight to count more than the first, the equivalence conditions of the second count more than tight, the equivalence conditions with more than the first count more than tight tight the second count, and the relationship between meet separation conditions, the Locale more than more than$tight tight yuan and generate Locale is the nature, the end of the article in the discussion of the element more than compact mapping problem, this paper presents under what conditions the inverse of the compact element like a compact element.The main conclusion:Theorem2.1.7:L is generated by co-compact element, L is the space of type.Theorem3.2.6:The co-compact second count must be the co-compact first count.Theorem3.2.7:T2space topology is the co-compact second count iff exit countable and compact set B={Bi|i∈ω,for arbitrarily non-emept closed C in X,exit Bo∈B so that∪B0＝C...