Tagged Questions
2
votes
4answers
156 views
Motivation for the importance of topology
Starting from tomorrow, I will be tutoring some undergraduate students following a course in general topology. I am looking for examples motivating the importance of topology in mathematics which can ...
1
vote
1answer
179 views
Compact and Locally Compact Spaces
I would like to consult with anyone who is reading this post on how do you explain the distinction between compact spaces and locally compact spaces to students who had just completed topology course ...
17
votes
8answers
2k views
Why do introductory real analysis courses teach bottom up?
A big part of introductory real analysis courses is getting intuition for the $\epsilon-\delta$ proofs. For example, these types of proofs come up a lot when studying differentiation, continuity, and ...
2
votes
1answer
96 views
weakly locally one-to-one?
Is there any standard name for this concept that is weaker than local one-to-one-ness?
In some open neighborhood of $x_0$ there is no point $x\ne x_0$ such that $f(x)=f(x_0)$.
Or, if you like: In ...
22
votes
5answers
1k views
Quotient geometries known in popular culture, such as “flat torus = Asteroids video game”
In answering a question I mentioned the Asteroids video game as an example -- at one time, the canonical example -- of a locally flat geometry that is globally different from the Euclidean plane. It ...
