Youtor
>> YOUR LINK HERE: ___ http://youtube.com/watch?v=BKvdhNkdDTs
This is the first video on a series of lectures on (Point Set) Topology. After definition a topology on a set, our focus is on a list of well-chosen examples. All future concepts in Topology will be illustrated with these examples. • • A Sincere Advice: Please watch the first 4 videos on the series on Metric Spaces up to the properties of the class of open sets in metric spaces. I shall assume this background in the course. • • A Warning: Most of the Indian teachers and books still hang onto the notions, concepts and results which were explored and formulated when the subject Topology was evolving and in a nebulous state. Now the dust has settled and the professional topologists across the world focus only on those concepts which have uses in other fields and which are essential for advanced topology such as Algebraic and Differential topology. So, you may miss many concepts which are taught in your course. But believe me that if you learn the contents of the videos you will be very confident of Topology either as a core course which is applied in other branches of mathematics or a stepping stone for advanced concepts. • • 0:00 Introduction • 0:45 Lecture Begins • 1:20 A very important remark on (point set) topology before delving into the subject • 7:20 Recall: The topology determined by a metric d on X • 12:58 Definition of a topology • 16:11 Topological Space • 16:42 The first Example of a topological space (Metric Space) • 18:21 Example 2 (Discrete Topology) • 21:13 ***The Trade Secret ! • 26:30 Example 3 (Indiscrete Topology) • 30:52 Example 4 (Analogous version of Ray Topology on the set of natural numbers) • 41:51 Example 5 (Ray Topology on R)
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