Understanding Compact Sets

In this video I explain the definition of a Compact Set. A subset of a Euclidean space is Compact if it is closed and bounded, in this video I explain both with a link to a specific video about closed sets below.

Video explaining Epsilon Neighbourhood and Closed Set:

[adeelakhtar]

Compactness has to to defined using open covers and subcovers. Of course, the characterization discussed in the video is true, but only valid for R^n, as stated by Heine–Borel theorem. Great video, thanks 😊

[markovchebyshev]

Really great video. It really explains with visual aid what finite subcover is

[PunmasterSTP]

Compact? More like "Completely where it's at!" This was a great video, and I'm really glad that you decided to make it.

[samtux]

I got the definition, but I have a question.
"Most of the time" we deal with open set topology. It is "concidered nice and useful".
Why do we suddnly switch to closed sets here?
What are the benefits?

[yassinesafraoui]

how can a set be closed and not bounded? does anyone have any example, because if there isn't any example, the condition of bounded would be useless then!

[franciscoabusleme]

This is not true in general, but it is true for Euclidean space...

[letseconomics]

How can we prove an algebraically production set is a closed set?

[wuwu]

not good ，pls tell open and bound set is not compact.

[rajtilakpal]

Seriously, you need to speak at a lower voice😅