The Filtered Description Of T₂ Locale

The pointless description of axioms of separation, especially T2 axiom is a question without final result in pointless topology. Combined with the analysis of all the existed theories, some new conditions of T2 Locale are given, and axiom is discussed in-depth. Here is the outline of the thesis:1.All possible choices of the description of T2Locale are analyzed, and a series of axioms is introduced, and the relation among them are discussed. 2. The properties of Locale are studied, and some satisfying results are obtained. For example, para compact Locale is regular, and is collection wise normal3. The definitions of T2※ and in [23]are analyzed, and some questions in expression are pointed out. After proper revision, a new brief description is obtained. The proof of a main conclusion is also questioned.