Introduction to Topology with Examples

This is a short introduction to topology with some examples of actual topologies. I hope this video is helpful.

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Thank you:)

[LucasDimoveo]

I'm excited for this! We need more higher level math tutorials/lectures

[randomblueguy]

Hello, I'm self-studying topology and I find this video extremely helpful, thanks. Though, I hope you would present in future videos more intuition as to why we choose to define things in some particular way, rather than any other way. I think that would be even more helpful.

[freebiehughes]

I hope you have videos on proofs for beginners! 😁 I'm not a math major, and Im not in school, but I believe I can learn this material fairly well before enrolling!

[MrChandrush]

That's clear and without mathematician arrogance. :) Thank you!

[freebiehughes]

Whoo, Hoo! Topology lectures! Thank you for posting!

[sebastiangarciaacosta]

No way! Today I had my first topology class, and I was kind of overwhelmed with the abstract definitions. This video is conveniently helping me. Thank you, Math Sorcerer!

[bebarshossny]

I don't understand the last example
How can tau be a topology on x if it doesn't contain the Set X itself
Like say we have the set {a, b, c} = X and we take X\{c} then we have {a, b}
Then we take {empty set} U {{a, b}} = {empty set, {a, b}}
No {a, b, c} there so it doesn't meet our rules
What am i not seeing?

[guitark]

I'm subscribed, don't quit math and making videos

[Kristielina]

very interesting topic. thank you for the explanation : )

[bebarshossny]

i always wanted to learn about topology but they don't offer the course for engineering students
i gotta pick up a book. please make more topology videos that would be awesome

[Ricocase]

Nice. Why is topology important? What does it do?

[hamzasehavdic]

I'm so excited to get back in this when I'm ready. Commenting to my future self.

(02/04/2021)
How you finding topology hums?

[martinhawrylkiewicz]

It's important to realize that we need finite intersections of open sets, to be open but arbitrary intersection of open sets need not to be open! Ex. Intersection of {-1/n, 1/n} as n goes to infinity ...= {0} which is not open!

[DesireeLekamge]

whats a countable subset of x mean? thanks!

[Lhosal]

This is amazing ASMR for me for some reason.

[zapazap]

Nice.

To play about with this: The cofinite topology on N might be easier for a beginner to grasp than the cocountable topology on R, while developing the same intuition. I might have added the the topology if intervals [a, inf) on R.

It would be nice for viewers to chime in with other examples of non usual topologies that are fairly easy to verify while at the same time pointing towards how topologies can be both strange and interesting, as opposed to contrived. (Not that contrived examples are bad. The {a, b, c, d} are probably de rigour for that purpose

Perhaps 'any set that is the union of open intervals' would be a good early example. It would prime the student for the idea of a basis without defining basis, but could be shown as an early example without much work.

Also: any similarly nice examples of product topologies that could be introduced at the beginning?

[amydebuitleir]

I'm guessing that the reason your definition doesn't need to explicitly require a finite set is related to the fact that intersection over an empty collection is problematic (Russell's Paradox).

[AKmacintosh]

For some reason I keep conflating set difference with intersection in my head, the example T={{a}, {a, b}, {a, c}, {a, b, c}, X, null} really triggered me until I realized that I am the idiot.

[asht]

I agree with how you define a topology on X. However, it is better if you incorporate the notation of the collection of sets such that the arbitrary union of sets is also in topology as well as the finite intersection of sets is also in topology.

[ismailtaskran]

I didn’t understand how the example in 11:50 is a topoloy for X. Don’t all topologies for X have to include also the set of X?