I am totally open to Dr Peyam's explanation of closed sets. Well done!

If you can find time in between your teaching and research, you should write a math text book. Maybe DE's.

Such an informative video! Thank you Dr. Peyam!!

I'm taking this course as a prerequisite for general relativity. Amazing videos.

@drpeyam

Жыл бұрын

Thank you!!

Thanks for the great video I have a question: In some references, there is a difference between the set of all limit (accumulation or cluster) points A' and the closure of a set "A bar". They define Closure of A (A bar)= union of A' and A I think A_bar=A' when we do not have isolated points.

Thanks. This video could be a very good start for topology.

Thank you! And please continue teaching us with so much passion! Amazing teacher and videos!

Excelent class of sets! Thank u man

[a,b] be like, all your limits ℝ belong to us.

very intriguing!

I found it a bit odd that open is defined by balls but closed is defined by sequences. So: a point x is a limit point of E if, for all r>0, there is a point in E in B(x, r). The proof that this definition is equivalent is like half the proof that the complement of an open set is closed and vice versa.

@drpeyam

3 жыл бұрын

I completely agree! The sequence definition is more practical, that’s why I started with it

You are a life saver. Thanks so much

@drpeyam

3 ай бұрын

Happy to help!

Ok. Thank you very much.

I'm taking Topology this semester at ASU; I didn't know you taught here!

@drpeyam

2 жыл бұрын

Woooow what a small world! I was there last year :) Enjoy your topology course!

Hi Dr Peyam Is N*(set of naturals without zero) closed in real metric?

@drpeyam

3 жыл бұрын

Yes, a convergent sequence of natural numbers is eventually constant, hence converges to a natural number. Same thing if you remove 0

One that is non-trivially openable and clopenable

What about not a ball but a sphere? Is that open?

If the complement of an open set is not open then what about R? R is open and its complement, the empty set, is open too.

@drpeyam

3 жыл бұрын

I said not *necessarily* open! It could of course be that the complement of an open set is open but it isn’t always the case

@greatstuff5

3 жыл бұрын

Sets are not doors

@greatstuff5

3 жыл бұрын

Remember complement of open is CLOSED not NOT OPEN. Not open and closed are different bro bro

@greatstuff5

3 жыл бұрын

Keep in mind one criteria for a topology on a set is that both the everything and nothing are elements of the topology, strictly via definitions this implies they are both closed sets as well as they are complements of one another. Sort of also in def of connected , it doesn’t assume the sets that form serparation need be closed it only assumes open but then by def they are both open and Thus clopen lol

@Happy_Abe

3 жыл бұрын

@@drpeyam oh my bad, thanks for the clarification!!!

Include all your own limo points?

Equal your closure ?

Complement of an open set ?

Crack!!!