Topology Definitions: Closure, Boundary, Interior

An explanation of how to define closure, boundary, and interior in topology using open and closed sets instead of a metric. Also explains adherence points. Intended as an introduction to basic concepts in topology.
0:00 Intro
1:24 Closure
7:46 Boundary
11:05 Interior
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Music: C418 - Pr Department

[@srijanchakraborty203]

Loved this lecture.... so clear and insightful. I hope you continue to make amazing content like this.

[@jorgeuliarte2641]

Excellent video, do you have a incredible capacity to explain yours lessons . Thanks for sharing your knowledge. From Salzburg, Jorge.

[@GutReconIkaros]

Looks like we are going to have a series of videos about topology :))

[@Iponamann]

Just in time - I’m taking the class right now :)

[@sumers9396]

perfectly explained! keep up the good work!!

[@khemlata3695]

Hey! Thank you for the lecture. I finally understood the concept.

[@claudefazio]

I taught myself topology 3 decades ago. I wish I had had your videos to teach that subject to me! You are a master higher math teacher. You make complex concepts very clear and you also motivate abstract definitions, which many textbooks on topology fail to do. Keep up the good work!

[@ms.bhuvaneswari5843]

What is U6 ? Sir

[@joshbolton2782]

Great explanation, Great video. Thank you sir!

[@ikechukwumichael1383]

Thank you. Now I have a clear grasp of the concept

[@nancymwangi9652]

loved the video, currently taking topology and it was a mess before i reached here👌

[@dewittreeve4345]

Very well done.

[@matti1610]

Nice video!

[@julianavarela4936]

I fell in lovee, you're a savior

[@voldemort2609]

Nice video! The idea of points being closed, if they are contained in many open sets is amazing (I have never thought about it this way)!
However talking about the closure without defining open sets on the numberline can be confusing. It would be interesting to see connections between metric and open sets.

[@MuPrimeMath]

Ā = A ∪ ∂A holds for all topological spaces.

[@voldemort2609]

@@MuPrimeMath Right, my mistake

[@AblieFatty-pb3ds]

you are so good

[@bencheesecake]

This feels like I missed the first week of lectures in a topology course. The definition of topology/open sets is a really important precursor to this material, and also one of the biggest challenges to students just startgin a topology course. I think this is good content, but needs to be video 2 or 3 in a topology playlist, and I can't find a precursor on your channel.

[@MuPrimeMath]

This video is directed toward people taking a topology course who are confused about these definitions in particular, so that's why I glossed over the preliminaries!

[@weirongwu4964]

Absolutely amazing video, thank for making this! The whiteboard looks awesome to do math on, what white board do you use?

[@MuPrimeMath]

I'm using a Writeyboard, which goes onto the wall!

[@debjitmullick7004]

Sir...1:10 does this open set means some thing like (a,b) as in Real Number space...?

[@MuPrimeMath]

We can define a topology on any set, so the points in the open sets can be anything we want! Like you say, one possibility is that the points are pairs (a,b) of real numbers. The example that I use in the video is a topology on the real number line.

[@bjornchan3083]

Nice vid for math dummies like me :)

[@ms.bhuvaneswari5843]

What is U6 sir

[@arfeenkhan2738]

Hey watching you from.Pakistan❤
Can you share another example of boundary point

[@mottkey9122]

1:26 A number line from positive infinity to negative infinity sounds very unnatural.

[@mottkey9122]

Well. Awful presentation. You Say one thing but show a different one and misuse simple definitions.