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10h
comment Two questions in the 'Real and Complex Analysis, Rudin'
It's better to make your questions self-contained. Include the text of the exercise itself instead of referring to page numbers. Also, don't group unrelated exercises into one question.
15h
comment Showing $\mathbb{R}$ is a completion of $(\mathbb{Q}, | \cdot |)$
Doesn't the book define $\Bbb R$ at all? What book is it?
16h
comment Showing $\mathbb{R}$ is a completion of $(\mathbb{Q}, | \cdot |)$
@LonelyMathematician It is important because $\Bbb R$ is usually axiomatically defined and/or constructed to be the completion of $\Bbb Q$.
1d
comment Uniform convergence of geometric series
@ellya Yes if you assume $|z| < |a| < 1$ for some $a$.
Apr
17
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?
Apr
16
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.