The Chainable Metric Spaces and Sets

The primary objective of this research work is to generalize the study of e-chains between two points to two sets in metric spaces. This generalization yields a characterization of e-chainable sets in terms of e-chains between points and sequences In chapter 3 we investigate the relation between compact sets and e- chainable sets and define self- chainable sets uniform chainable sets strongly chainable sets with examples and prove fixed point theorem. After this in chapter 4 we define locally chainable sets in metric space and prove various new results. In chapter 5 The notion of locally chainable metric spaces is introduced. In chaper 6 The concept of paths and homotopy in metric spaces have been generalized to c-path and c-homotopy and path chainable spaces have been defined. In the last chapter we extend the concept of e-chains in the 2- metric space and prove their characterizations in terms of chainable sets.