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6h
comment Every non-constant closed curve has positive period
If $T$ is negative, why don't you just take $-T$ instead?
1d
comment Sphere homeomorphic to interval times space
Perhaps I misunderstand the question, but does $I$ denote $[0,1]$ or $(0,1)$? If the former (the standard use of the notation $I$), this is clear since $\mathbb{S}^n$ has no boundary (whereas $I\times Y$ does), and in the latter, this is also clear since $I\times Y$ is not compact.
Jan
18
answered Can we see this integral as the line integral of a 1-form
Jan
13
revised Is the metric on the circle, induced from the plane, not a flat one?
added 586 characters in body
Jan
13
answered Is the metric on the circle, induced from the plane, not a flat one?
Jan
12
awarded  group-theory
Jan
8
comment Prove the set of continuous real-valued functions on the interval $[0, 1]$ is a subspace of $\mathbb R^{[0, 1]}$.
Hi @copper.hat, thanks for your comment! You're right that, assuming $U\neq \emptyset$, (2) follows from (1) (there are a number of ways of proving this, e.g., what you suggest). However, it doesn't follow from (1) alone if $U=\emptyset$ ((1) is vacuously satisfied if $U=\emptyset$). I guess the entire point of (2) is to ensure that the empty set is not a subspace of any vector space.
Jan
8
comment Prove the set of continuous real-valued functions on the interval $[0, 1]$ is a subspace of $\mathbb R^{[0, 1]}$.
I don't understand the downvote; I think this seems like a perfectly reasonable question. I also don't understand the vote to close; the OP has indicated an attempt to solve the question (which is essentially correct).
Jan
8
answered Prove the set of continuous real-valued functions on the interval $[0, 1]$ is a subspace of $\mathbb R^{[0, 1]}$.
Jan
3
comment How to compute the fundamental group from first homology group?
I know this answer was posted a long time ago (and it's a great answer!) but, regarding the knot theory comment, perhaps it is worth stating that a knot complement is determined by the map (induced by inclusion) $\pi_1(\partial K)\to \pi_1(K)$, where $\pi_1(\partial K)$ denotes the peripheral subgroup of $\pi_1(K)$ (the fundamental group of the torus boundary of the knot complement). I believe this is a result of Gordon-Luecke (for the unknot, it is still non-trivial - in this case, it is a corollary of the sphere theorem in 3-manifold topology).
Jan
2
reviewed Reviewed Finding the dimensions of the the right circular cylinder of greatest volume
Jan
2
revised Finding the dimensions of the the right circular cylinder of greatest volume
fixed grammar
Jan
1
comment Classification theorem for vector spaces
Hi @user254665, thanks for the comment! You're right, of course. I replaced $\aleph_1$ with $\mathfrak{c}$, the cardinality of the continuum. Happy new year!
Jan
1
revised Classification theorem for vector spaces
added 67 characters in body
Jan
1
answered Classification theorem for vector spaces
Dec
31
comment find an irreducible polynomial
Hi @Alex, sorry! I've had that happen to me before. I think there should be some form of notification that someone else is writing an answer to a question if you are in the process of doing so. (I'm not sure if this was discussed on meta at any stage.) Of course, if there could be many good, alternate answers to one question, this could be problematic, so I'm not sure how one would implement such a system appropriately. (But with questions like this, where almost a one sentence answer suffices and there aren't really that many alternatives for answers, it might be useful.) Happy new year!
Dec
31
answered find an irreducible polynomial
Dec
30
comment A $T_0$ topological vector space is Hausdorff
Hi @Silvia, that makes sense, thanks for the clarification.
Dec
30
comment A $T_0$ topological vector space is Hausdorff
Hi @Alex, you're right! Thanks for the correction.
Dec
30
revised A $T_0$ topological vector space is Hausdorff
added 7 characters in body