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I'm a student of mathematics in Germany.


5h
comment Is there a general notion of orientability, e.g. for the rationals?
@QiaochuYuan Okay, thank you anyways.
5h
comment Is there a general notion of orientability, e.g. for the rationals?
@QiaochuYuan I wouldn’t know, I don’t even care about the pragmatic use of such a notion. I was merely hoping for any sort of definition for orientability, (a) applicable to unusual, yet imaginable spaces like $ℚ$, (b) fitting well with the intuition for these spaces, and (c) generalising the usual notion for orientability for manifolds.
5h
comment Is there a general notion of orientability, e.g. for the rationals?
@QiaochuYuan I was coming from a more intuitive view point, regarding an orientation of a line as a choice of “left” and “right”, which should be possible for the ratonal line as well. Perhaps my notion of orientation is too naïve?
6h
asked Is there a general notion of orientability, e.g. for the rationals?
Nov
25
revised Instructive sources for arguing without elements
edited tags
Nov
25
comment Suppose that $N_1$ is a normal subgroup of $G_1$. Is the image $f(N_1)$ of $N_1$ a normal subgroup of $G_2$?
No. Take a group $G$ which has a non-normal subgroup $N ≤ G$. Then take $G_1 = N$, $G_2 = G$ and $f = \text{inclusion}$.
Nov
24
comment Is there are “sphere” associated to any topological vector space?
… with “yes”, you won’t have to go specifically into the notion of “sphere-like objects”, with “no” you would have to. So the vagueness of sphere-like objects only becomes critical if the answer really is “no.” (Now I’m going to sleep.)
Nov
24
comment Is there are “sphere” associated to any topological vector space?
That was only a joke, of course, so let’s not get into that too deep, but the point I was trying to make is that, in my view, this question can be answered if and only if it can be answered positively (because such an answer would consist of some sort of construction of a sphere-like object which would most likely satisfy your curiosity). If the answer is “no,” then it seems utterly hopeless to devise a sufficiently precise notion of sphere-like objects and prove that there isn’t a definite way to associate such sphere-like objects to topological vector spaces.
Nov
24
comment Is there are “sphere” associated to any topological vector space?
This question is too vague if and only if its answer is “no.”
Nov
24
comment Closedness and boundedness in metrizable topological spaces
It’s not, no. There’s no reasonable way of interpreting “boundedness” in arbitrary topological spaces.
Nov
24
comment Show that it is/is not a normal extension
What’s a canonical extension? Oh, you probably mean a normal extension!
Nov
24
answered Closedness and boundedness in metrizable topological spaces
Nov
24
answered Periodic functions and limit at infinity
Nov
24
answered Creating surjective holomorphic map from unit disc to $\mathbb{C}$?
Nov
24
comment Extension theorem for locally Lipschitz functions
Isn’t $(0..∞) → ℝ,~x ↦ 1/x$ locally Lipschitz?
Nov
24
comment How prove this $n$ smaller cubes ( length is $1,2,3,\cdots,n$) can't Mosaic a big cube
@Henry: This is probably implied by “length is $1, 2, 3, …, n$.”
Nov
22
comment Solving $(1-x)^3 = -1$ over the complex field
Do you want a solution in the form of $a + ib$? Can you guess the solutions for $z^3 = -1$ by geometric interpretation?
Nov
21
answered Find remainder when $2^{30}\cdot 3^{20}$ is divided by $7$ without using calculator
Nov
18
comment Why is $0^0$ also known as indeterminate?
You will need to explain the bar notation a bit more. Is $1||4^0 = 1·4^0$?
Nov
18
comment Fundamental group of sphere
@Sasha $π_1(S^2) = \text{trivial group}$ and $\text{trivial group} × ℤ = ℤ$. You can write the trivial group as $0$ or $1$ (depending on whether you want to write your group operations multiplicatively or additively).