1d
comment Show that in ℝ[x], no polynomial of odd degree > 1 is irreducible.
This is usually proved using the intermediate value theorem. Do you have access to this theorem?
2d
awarded Nice Answer
2d
comment Question about degrees of maps from $S^1 \rightarrow S^1$
Yes. Looks good. However, I would avoid using $*$ for multiplication as it has other meanings. Use \cdot or \times instead.
Apr
15
comment Integral of $\sin|x|$
The last integral diverges.
Apr
7
comment Can euclidean space be written as $X \times X$ for some topological space $X$?
I don't see how this proof works. Can you explain the "You can show" part?
Apr
7
comment Can euclidean space be written as $X \times X$ for some topological space $X$?
That MO thread does answer the general question.
Apr
7
comment A simple fundamental group
See this answer for the universal cover of your space. From the group action described in that answer, it follows that the fundamental group is $\Bbb Z$.
Apr
5
reviewed Approve suggested edit on explore the convergence of series with ln(n)
Apr
5
comment Examples of Functions
Do you have any thoughts on any of the questions? Is the first question possible at all?
Apr
5
answered Prove Simply Connected
Apr
5
comment Is Orbit Criterion an abstract nonsense? Different induced fundamental groups.
@108592 Both examples fulfill the assumption you have. In the first example, let the covering space $Y$ be the disjoint union of a circle and line. The circle is mapped to $X$ via the identity map. The line is mapped to $X$ via the map $p(x) = e^{2\pi ix}$ as you suggest. The pre-image of a point of $X$ is the union of infinitely many points from the line and one point from the circle. If you choose $\tilde q$ from the circle and $\tilde q'$ from the line (both on the same fiber), then $p_*(\pi_1(Y, \tilde q))$ is infinite cyclic, whereas $p_*(\pi_1(Y, \tilde q'))$ is trivial.
Apr
5
comment Image of Regular Map
$A^2$ can mean a number of things. Is it the Euclidean plane here?
Apr
5
revised Is Orbit Criterion an abstract nonsense? Different induced fundamental groups.
added 538 characters in body
Apr
5
answered Is Orbit Criterion an abstract nonsense? Different induced fundamental groups.
Mar
30
revised strong deformation retract, of a perforated plane?
added 218 characters in body
Mar
30
answered strong deformation retract, of a perforated plane?
Mar
29
comment The Cantor set is nowhere dense
Did you prove that $C$ is closed? Nowhere dense means that the closure has empty interior. Your proof is OK as long as you show that $C$ is closed.
Mar
29
comment Prove: Let $I \subseteq \mathbb R$. If $f: I \rightarrow \mathbb C$ is differentiable on $I$ with $f'(x)=0$, then $f$ must be real.
@DanielFischer Makes sense. This is probably what the author meant.
Mar
29
revised Prove: Let $I \subseteq \mathbb R$. If $f: I \rightarrow \mathbb C$ is differentiable on $I$ with $f'(x)=0$, then $f$ must be real.
You don't need a ^ in f'(x)
Mar
29
comment Prove: Let $I \subseteq \mathbb R$. If $f: I \rightarrow \mathbb C$ is differentiable on $I$ with $f'(x)=0$, then $f$ must be real.
Are you sure you aren't missing something? $f(x) = i$ isn't real, but $f'(x) = 0$. What's the context of this question? Is it from a book?
1 2 3 4 5