Studies Of The Relative Questions About Measurement On A Domain And Domain Environments Of Topological Spaces

Domain theory that ocurred in 1970's plays a fundamental role in denota-tional semantics of Programm languages.The basic character of this theory is that order and topology are combined and act on each other,which becomes the field that is concerned by computer scientists and topologists.It builds relations between this theory and other mathematical principles.Keye Martin firstly researched metric of information of every element on a domain and the degree of approximation and convergence in his desserta-tion for PhD in 2000 where he defined the concepts such as measurement,u topology,informatic derivative,and so on. Based on these ideas he established a comparatively complete analysis where in particular he studied proerties of topological spaces with G@ Domain models by measurement.Influenced by the work, We investigated three parts below:1. We studied measurement on a w continuous domain and gave several sufficient conditions that G@ lemma hold valid.We discussed some properties and applications of measurement satisfying triangle inequality.2. We gave some results about u topology and informatic derivative and in particular obtained a sufficient condition that makes u topology become second countable.In this way ,we answered the relative quetions raised by Martin in 2000.3. We showed some equivalent characterizations that Tychonoff spcaes are compact spaces and investigate properties of topological spaces which admit domain models.