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geocalc33

09:06

-1

Q: Each "octant" of $\Bbb S^3$ is diffeomorphic to $\Bbb R^3.$

I'm thinking of a space $\Bbb S^2$ in which each "quadrant" of $\Bbb S^2$ is diffeomorphic to $\Bbb R^2,$ and a space $\Bbb S^3$ in which each "octant" of $\Bbb S^3$ is diffeomorphic to $\Bbb R^3.$ To clarify, the "quadrants" and "octants," are disjoint submanifolds whose union's closure is the w...

thoughts on how to improve?

5 hours later…

user1729

13:51

@geocalc33 I think you need to make clear what you know. Have you looked in any standard books or found any papers which you think might be related? Or are you just a first year undergrad. fishing for a topic?

Vamsi Krishna

math.stackexchange.com/questions/2270276/…≤-20/3745964#3745964

I answered this question but got a downvote. Any constructive suggestions?

Arctic Char

@VamsiKrishna Did you just got downvoted?

Vamsi Krishna

Yes.....but actually I was pretty satisfied with my answer and was already sad on not getting any upvotes.....the downvote kind of troubles me

@ArcticChar

Just to confirm, this is the place for constructive suggestions on Q and A right?

Arctic Char

14:06

Yes this is the right place to ask.

Vamsi Krishna

@ArcticChar Thanks!

Arctic Char

@VamsiKrishna concerning your answer, I think all three of the answers there used the same observation. And to me this answer already summarize that nicely.

geocalc33

@user1729 that's a good point thanks

I'll keep that in mind next time I ask a question

Vamsi Krishna

@ArcticChar Oh okay yeah. So from next time I answer only if my points totally differ or adds more essential context to a previous answer?

Arctic Char

14:31

@VamsiKrishna Yes, definitely. (I am saying that this has to be the reason for the downvote, which we don't really know)

Vamsi Krishna

@ArcticChar Thanks for your help! Had an amazing first experience here!

Arctic Char

14:48