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1d
comment Definable over $(\mathbb{R}, +, \cdot)$
Where is the existential quantifier for $v_{1}$ in (c)?
2d
comment Free action of a discrete group gives a covering space
What if $\mathbb{Z}$ acts on $S^1$ via irrational rotations? The quotient is compact but not Hausdorff.
May
1
awarded  Nice Answer
Apr
19
comment Show that $f$ is identically zero if and only if $\displaystyle \int_{a}^b f(x)dx = 0$
Yeah, I just edited that back in. Thanks for pointing this out!
Apr
19
revised Show that $f$ is identically zero if and only if $\displaystyle \int_{a}^b f(x)dx = 0$
added 142 characters in body
Apr
19
comment Show that $f$ is identically zero if and only if $\displaystyle \int_{a}^b f(x)dx = 0$
Oh right, I misread the assumption.
Apr
19
answered Show that $f$ is identically zero if and only if $\displaystyle \int_{a}^b f(x)dx = 0$
Apr
18
answered Why is a line not quasi-isometric to a plane?
Apr
12
answered Orientable on almost complex manifold
Apr
7
answered Why is the absolute of the union of the differences of sets greater than the absolute of the difference between the unions?
Apr
7
answered The set X is the complex numbers in cofinite topology
Apr
7
answered Why if $p (x_1, \dots, x_n)$ is polynomial on $\mathbb{R}^n$, then $p (x) \neq 0$ is satisfied by open dense set?
Apr
1
comment Does it make sense to define a “metric topological space” $(M, d, \tau)$
They are both topological notions, but in general they do not coincide. There are spaces which can be sequentially compact but not covering compact, and vice-versa. However, for metric spaces they are the same. In any event, sequential compactness is just about covergence of sequences, it doesn't require us to define a metric.
Apr
1
answered Does it make sense to define a “metric topological space” $(M, d, \tau)$
Mar
12
answered Unique way to show $S^n$, $n \geq 2$ is simply connected.
Mar
10
comment Can $S^n$ be defined without reference to an $n+1$ dimensional embedding space?
Oh, oops. Yeah, I corrected that.
Mar
10
revised Can $S^n$ be defined without reference to an $n+1$ dimensional embedding space?
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Mar
9
answered Can $S^n$ be defined without reference to an $n+1$ dimensional embedding space?
Jan
26
awarded  Famous Question
Jan
23
awarded  Good Answer