Manifolds 2 | Interior, Exterior, Boundary, Closure [dark version]

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This is my video series about Manifolds where we start with topology, talk about differential forms and integration on manifolds, and end with the famous Stoke's theorem. I hope that it will help everyone who wants to learn about it.
x
#Manifolds
#Mathematics
#Differential
#LearnMath
#Stokes
#calculus
I hope that this helps students, pupils and others. Have fun!
(This explanation fits to lectures for students in their first and second year of study: Mathematics for physicists, Mathematics for the natural science, Mathematics for engineers and so on)

[@fizikchy]

Thanks for lectures. Are the two Measure Theory videos put to this playlist accidentally? Or are they a part of Manifoldsd lectures?

[@brightsideofmaths]

Thanks for telling me! This was my mistake :)

[@xinglinli9874]

What's the difference between accumulation points and limit points?

[@brightsideofmaths]

They can describe the same thing.

[@surendranmurugesan]

So an accumulation point cannot lie outside S and inside U?

[@brightsideofmaths]

An accumulation point can lie outside, yes :)

[@surendranmurugesan]

@@brightsideofmaths Thanks. Does your case include that as well? It did not feel obvious to me (when the point was inside) although you might have meant it.

[@mathesonnenseite]

What do you mean? The assumption is that p is an element of X.@@surendranmurugesan

[@surendranmurugesan]

Imagine the following situation. Point 'p' lies inside X and inside U. But outside S. Is this still an accumulation point?@@mathesonnenseite

[@robn2067]

What is the difference between the "dark" version and the "blue" version?

[@brightsideofmaths]

There is no blue version anymore. Just dark version and bright version :)

[@richardfrangie3518]

[@surendranmurugesan]

At 5:28 why not write for case (b) as U n S = \phi

[@brightsideofmaths]

We use the same notation as in (a) :)