The Open Ball in a Metric Space X is Open in X

In this video I prove that the open ball centered at x of radius r, B(x, r), is an open subset of the metric space X.

If you enjoyed this video please consider liking, sharing, and subscribing.

There are several ways that you can help support my channel:)

************Udemy Courses(Please Use These Links If You Sign Up!)*************
Abstract Algebra Course

Advanced Calculus Course

Calculus 1 Course

Calculus 2 Course

Calculus 3 Course

Calculus 1 Lectures with Assignments and a Final Exam

Calculus Integration Insanity

Differential Equations Course

Differential Equations Lectures Course (Includes Assignments + Final Exam)

College Algebra Course

How to Write Proofs with Sets Course

How to Write Proofs with Functions Course

Trigonometry 1 Course

Trigonometry 2 Course

Statistics with StatCrunch Course

Math Graduate Programs, Applying, Advice, Motivation

Daily Devotionals for Motivation with The Math Sorcerer

Thank you:)

[basicallymath]

Hi! Awesome video, could you do a proof for why in R^n, the interior of B[x, r] = B(x, r)? Amazing channel too!

[DeuschtePS]

Who's watching this video in 2024? ❤

[rgentil]

evening, do you have an elementary topology playlist? i am studying continuous funcitons, homeomorphisms, boundaries, etc

thank you

[paulogramacho]

Have you ever proved that sqrt(2) is irrational in your channel? That is a good proof.

[manabhanjandas]

Saturday I have paper on metric spaces can I get some more videos on continuity on metric spaces please 🥺

[hunternegron]

Lovely proof! I will say that I think "Y contains all its interior points" is misleading phrasing because it could be interpreted as "every interior point of Y is an element of Y", when we really want to say "every point of Y is an interior point" which I don't think are the same. It's a minor thing but may cause of confusion.

[nixoop]

Hi maths sorcerer I'm 16 years old and struggling to with this one integration quesiton I just can't get the answer probably novice level for you . I'm off school I'll and can't get help. its the integral of cosx over cos ^ 2 (x / 2) could you send me the worked solutions to my email or something? Thank you :)