The Coherention Of Locale And Topology Spaces

In locale categories (or its dual category, the category of frame), discussion and research for topology locale theory provides an important research means-in the locale fully from the collection in the locale of open sets to its nature. For the study of the topological structure, a locale theory not only opened up a new perspective, but also enriches and develops the topology.A functor from a category mapped to another category, if meets some conditions, we can define it for expansion functor, for expansion overall functor compatibility and saturability, stability is all know we study object, this paper mainly studies for the some of the examples and relationship.For the expansion coherentily functor,it is compatible saturated; For its stability, this gives object stable several equivalent conditions and sufficient conditions such as prime T1 or prime T2; For the stability of the topological structure of the research also given conditions of equivalences, for example in a frame each element is compact or each ideal is principal ideal.