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May
14
comment Are there compact manifolds without boundary?
Ah, know now where my confusion came from (But first: Thank you for your detailed comments and fine explanations!). I wrote "$S^{n-1}$" but in my head I pictured $S^1$ embedded in $\mathbb{R}^2$. In this special case, I believe my observations from above should hold true, right ?
May
13
comment Are there compact manifolds without boundary?
One last question, to make sure I understood: Does that mean that if we don't allow (sub)manifolds with boundary, then except $S^{n-1}$ itself (and perhaps $\emptyset$ which I shall exclude from consideration as a pathologicality) there aren't any compact submanifolds of $S^{n-1}$ ? $$$$Because every submanifold is obtained by intrsecting an $R^n$-open set with $S^{n-1}$, but a set obtained in such a way is not closed, thus not compact.$$$$If we do allow (sub)manifolds wit boundary, the intersection of closed sets, like $R\times [0,1]$ with $S^{n-1}$, would yield a compact submanifold, right ?
May
13
accepted Are there compact manifolds without boundary?
May
13
comment “Nullifying” an ODE
ok, having a (negative) answer from authoritative user is itself a valuable information. thank you.
May
13
accepted “Nullifying” an ODE
May
12
asked “Nullifying” an ODE
May
12
asked Are there compact manifolds without boundary?
May
7
comment Let $M\subseteq \mathbb{R}^k$: Manifold topology vs. trace topology
yes, I mixed the definitions up, my bad. (you're a good explaner, it seems)
May
7
accepted Let $M\subseteq \mathbb{R}^k$: Manifold topology vs. trace topology
May
5
comment Let $M\subseteq \mathbb{R}^k$: Manifold topology vs. trace topology
Could you elaborate that a bit, please ?
May
5
revised Let $M\subseteq \mathbb{R}^k$: Manifold topology vs. trace topology
added 1 character in body
May
4
asked Let $M\subseteq \mathbb{R}^k$: Manifold topology vs. trace topology
Apr
15
comment Short differential-form free route to understanding a specific surface integral
Here's your bounty, your answer was well worth it! If some differential-form free reference comes to mind, please let me know. Thank you.
Apr
15
awarded  Nice Question
Apr
14
comment Short differential-form free route to understanding a specific surface integral
No, I keep my word, your answer really was so enlightening, that I can at least spare 50 rep points, I just have to wait 22 hours until the reward can be given. I can only hope that for some of my future questions someone like you (or you) is going to be among the answerers. Do you perhaps know of a text in a general integration theory (over manifolds in $\mathbb{R}^n$, though I'd be also happy with some special case of that - like treating only surfaces, i.e. only $(n-1)$-dimensional manifolds in $\mathbb{R}^n$) is presented, like you did, without appealing to differential forms ?
Apr
11
comment Short differential-form free route to understanding a specific surface integral
Such a great answer! Tomorrow, when I can award the bounty (I have to wait 48 hours after the question has been asked to award it), you will get it.
Apr
11
accepted Short differential-form free route to understanding a specific surface integral
Apr
10
asked Short differential-form free route to understanding a specific surface integral
Apr
9
awarded  Nice Question
Apr
8
comment Omega limit set vs. stable manifold of a point?
Could you please answer my two questions ? That would be great.