Math 101 Fall 2017 112917 Introduction to Compact Sets

Definition of an open cover. Definition of a compact set (in the real numbers). Examples and non-examples. Properties of compact sets: compact sets are bounded. Compact sets are closed. Closed subsets of compact sets are compact. Infinite subsets of compact sets have accumulation points (compactness implies limit point compactness).

[thomashobohm]

I'm in an introductory analysis course right now using Lay's book, and your videos have been super helpful in supplementing my notes from class. Thank you for making your lectures public :)!

[jacekolchawa]

Thanks for those lecttures, they're really enjoyable. Two questions come to my mind ater watching that:
1) Regarding the proof that compact => closed. Is it really that obvious, for higher dimensions, that this smalles eps/2 does not inetrsect with K? on a line (in R^1) those "open disks" are ranges defined by points already excluded but in higher dimensions? it seems intuitive in R^2 but i just do not see the proof off of the top of my head?
2) in proof of closed subset of comppact set being also compact. Is it necesary to exclue that F'(complement of F) from the finite subcover we got? i mean it seems elegant, but if to any finite open cover G we add any set, lets say s=(1, 2) G \sum {s} stil remains finite?

[jainamkhakhra]

Thank you so much Professor!. Your lecture finally eases the notion of compact sets!!

[SoumyadeepDuttaIISc]

Hello Prof. Ou. Nice lectures. Is it possible to get a sorted list of the videos in this playlist. I am having difficulty in sorting them in order. I am planning to follow along these lectures along with you math 131 lectures. thanks.

[hkrish]

Hi, thanks for the video. May I know what book are you following.

[karimkaan]

you are an amazing teacher
you also give great content
i hope u more subscrs and viewrs😃