Generalizing Of Elastic Spaces

The study of metric spaces plays an important role in General Topology, and in the process of generalizing metric spaces, M1, M2, M3spaces and elastic spaces are found. They have some graceful properties and introduce to us several interesting problems.There are three chapters in this thesis, and we mainly focus on the gen-eralizing of elastic spaces.Chapter â…  is the Introduction. In this chapter we review the study of metric spaces, M1, M2, M3spaces and elastic spaces, the definitions of which are also given there. Then we discuss the methods to generalize these spaces, and give an open problem concerning them.In Chapter â…¡, we discuss the generalization of elastic spaces. The defini-tion of quasi-clastic spaces and several properties are given. At last, we give the definition and properties of Network-elastic spaces.In Chapter â…¢, the definition of proto-metrisable spaces is given, and using the method in Chapter â…¡, we give another theorem which can be used to decide whether a space is proto-metrisablc.