Analysis II Lecture 02 Part 1 basic topology of euclidean space

Some topological notions of Euclidean space are introduced.

This is part of a series of lectures on Mathematical Analysis II. Topics covered include continuous and differentiable multi-variable functions on Euclidean space, the chain rule, the implicit function theorem, manifolds, tangent spaces, vector fields, the degree and index of a smooth map, the Euler characteristic, metric spaces, the contraction mapping theorem, existence and uniqueness of solutions to ordinary differential equations, and integral equations.

I speak rather slowly, so you may wish to increase the speed of this video.

These videos were created during the 2017 Spring semester at the UConn CETL Lightboard Room.

[vinayseth]

Thanks for this! One question though-Is Euclidian Space continuous by its very nature? Did Euclidian say or imply anything about the same in his postulates and axioms?