General Topology

The aim of writing this book is to provide a good account of General Topology to master degree students of Indian universities. However, the book may be used partly for under-graduate students, wherever topology is taught. Chapter I gives a good account of Axio-matic Set Theory, thereby giving a good treatl ment of ordinal and cardinal numbers. The of ordinals provide good counter examples at several places for the development of the subject. In Chapter II, topological spaces are dealt with and open maps, closed maps and homeo-morphism are treated. Chapter III deals with weak and strong topologies and Quotient spaces. Quotient spaces provide good number of counter examples. Chapter IV deals with separation and countability axioms. A space which is completely regular but not normal due to A. Mysior is included. In Chapter - V. nets and filters are treated to study convergence in arbitrary topological spaces. In Chapter VI metric spaces are dealt with and Nagata - Smirnov metrization theorem is included. Chapter VII deals with compact spaces and its various weaker forms. like countably compact, pseudo-compact, feebly-compact. sequentially compact, A.-compact, locally compact etc. Finally the chapter ends with Baire spaces and H-closed spaces. Chapter VIII deals with connected spaces and includes countable connected space due to Golomb and Brown. This chapter also deals with locally connected spaces, path-connected spaces and Continua. In Chapter IX. we study totally bounded and complete metric spaces. ech complete spaces. Chapter X deals with paracompact spaces and some of its weaker forms. It also contains some more metrization theorems using sequence of coverings due to Arhangeskii. Bing, A. H. Stone. Moore-Morita, Hanai and V. K. Balchandran.