Lecture 19 02 21|| Totally Bounded Set (Part A)

This is the recording of online lecture (dated 19-02-2021) for the students of M.Sc Mathematics of Central University of South Bihar.
In this lecture we have covered following points:
(i) Bounded Set.
(ii) Diameter of a set.
(iii) Diameter is finite if and only if set is bounded.
(iv) Totally bounded set.
(v) Examples.
(vi) Totally bounded implies bounded.
(vii) example for converse of (vi) is not true.
(viii) In R with respect to usual metric a set is totally bounded if and only if it is bounded.
(ix) Subset of a totally bounded set is totally bounded.