19,300 reputation
42761
bio website ie.linkedin.com/in/aymanh
location Dublin, Ireland
age
visits member for 3 years, 4 months
seen 1 hour ago

15h
comment Is it true that $[0,1]\times [0,1]\cong \overline{B}(0,1)$?
See Lee's Introduction to Topological Manifolds for a more general result: Any compact, convex subset of $\Bbb R^n$ with non-empty interior is homeomorphic to $\overline B^n$. This is proposition 5.1 in the book.
20h
comment Prerequisite for Petersen's Riemannian Geometry
What do you mean by "avoids topology"? General topology is required for anything beyond the first chapter of Loring Tu's book. Furthermore, the book itself contains a quick review of some general topology topics in the appendix.
1d
comment Specific Retraction from $\mathbb{R}^2$ to the logarithmic spiral
@ShalinDoctor See my answer for two ways to approach this.
1d
answered Specific Retraction from $\mathbb{R}^2$ to the logarithmic spiral
1d
comment Specific Retraction from $\mathbb{R}^2$ to the logarithmic spiral
Transform the plane so that the spiral becomes a half-line, apply the retraction you have, and transform back using the inverse of the original transformation.
1d
answered Show polynomial is irreducible
1d
comment Does $\mathrm{Im}(f(z))$ bounded above $\implies$ $|f|$ is bounded, for analytic $f$?
@HagenvonEitzen Feel free to add it as another example. :)
1d
answered Does $\mathrm{Im}(f(z))$ bounded above $\implies$ $|f|$ is bounded, for analytic $f$?
2d
comment Specific Retraction from $\mathbb{R}^2$ to the logarithmic spiral
Start with a retract from $\Bbb R^2$ to the half-line $\{(x, 0) : x \ge 0\}$ and compose with a plane transformation that twists the line into the desired spiral. In fact, you can make this a deformation retract.
2d
answered Cohomology groups of real projective space
2d
comment Isomorphism between finite fields
The polynomials are reducible (both have $1$ as a root). Therefore the quotients aren't fields.
2d
comment Isomorphism between finite fields
The polynomials are reducible (both have $1$ as a root). Therefore the quotients aren't fields.
2d
comment Is every positive function defined from $\mathbb{N}$ with real values continuous?
If you give $\Bbb N$ the discrete topology, every function $f : \Bbb N \to \Bbb R$ is continuous.
2d
comment Galois Group Calculation
Switching $\sqrt 2$ and $\sqrt 3$ doesn't give you an automorphism fixing $\Bbb Q$. You want $\sqrt 2 \mapsto - \sqrt 2$.
2d
comment “Scaled $L^p$ norm” and geometric mean
@user92360 Study the function $x \mapsto \dfrac{|f|^x - 1}{x}$ as a whole. It is decreasing as $x \to 0$.
Apr
21
comment Question concerning the integrability of a function
You're welcome. I'll have a look and give it a try later today.
Apr
21
answered Question concerning the integrability of a function
Apr
21
comment Problem of BIG RUDIN: Chapter 3 , Q. 5 . last part
@user92360 I edited my answer to clarify this. In your question, you have the assumption that $\|f\|_r < \infty$ for some $r$. This gives you the dominating function.
Apr
21
comment “Scaled $L^p$ norm” and geometric mean
@user92360 I edited my answer to clarify this. In your question, you have the assumption that $\|f\|_r < \infty$ for some $r$. This gives you the dominating function.
Apr
21
revised “Scaled $L^p$ norm” and geometric mean
Improved style. Clarified an assumption.