An introduction to Point-Set-Topology Part - II

About

This course begins with the assumption that the audience has attended the part-I. We cover all important advanced topics such as various notions of compactness in metric spaces, Ascoli's theorem, paracompactness, compactifications, Urysohn's Metrization theorem, Stone-Weiertrass theorem, totally disconnectedness, etc. Checking whether any of these topological properties in product invariant occupies a considerable amount of our time. A brief introduction to Topological Dimension Theory, discussion of function-space topologies and the Ordinal topology as a rich source of counter examples are the added features. Finally the course ends with a brief introduction to topology of manifolds in which we discuss the 1-dimensional case completely and outline the 2-dimensional case. The content of this course will be useful for any body who wishes to study deeper aspects of analysis or topology or in applying topological tools anywhere else in Mathematics or Physics, etc. It is certainly useful in understanding the two courses that I have offered on Algebraic Topology on NPTEL portal.

Intended audience: Students from various streams which include some modern mathematics such as B. Sc., M. Sc., Students, Ph. D. , B. Tech. and M. Tech. who have seriously attended PST-I or have acquired the basic knowledge the content offers from elsewhere, will be able to benefit from this course.

Prerequisites: Students are supposed to have attended the part-I of this course from NPTEL or acquired the basic knowledge the content the part-I offers from elsewhere.INTENDED AUDIENCE: Students from various streams which include some modern mathematics such as B. Sc., M. Sc., Students, Ph. D. , B. Tech. and M. Tech. who have seriously attended PST-I or have acquired the basic knowledge the content offers from elsewhere, will be able to benefit from this course.