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math-physicist
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4 votes
0 answers
155 views

Show $\frac{FA^4}{AB^2}+\frac{FB^4}{BC^2}+\frac{FC^4}{CA^2}\geq\frac{FA^3+FB^3+FC^3}{FA+FB+FC}$ for $F$ the Fermat-Torricelli point of $\triangle ABC$

4 votes
1 answer
86 views

A (short) proof for the paracompactness of CW complexes

3 votes
1 answer
236 views

Prove that every compact manifold is homeomorphic to a subset of some Euclidean space.

2 votes
0 answers
165 views

Complete list of prerequisites to study "An Introduction to Riemannian Manifolds" by Lee.

2 votes
2 answers
203 views

Alternate proof of "$\ell^\infty$ is not separable".

2 votes
1 answer
171 views

How to find an analytic $f:G\to\mathbb C$, where $G=\{z:Re(z)>0\}$, such that $f(G)=D=\{z:|z|<1\}$ using a Mobius Transformation?

2 votes
1 answer
233 views

Prove that if $f=u+iv$ is conformal in $G\subseteq\mathbb C$, then the Cauchy-Riemann Equations hold for $u$ and $v$.

2 votes
4 answers
190 views

How to show that two certain chords of a circle passing through the incentre of a given triangle are equal?

1 vote
0 answers
63 views

How does a smooth functor guarantee the existence of another smooth vector bundle from a given one?

1 vote
1 answer
109 views

Understanding the CW decomposition of the real projective $n$-space

1 vote
0 answers
48 views

Is obtaining the closed form for a $k$-sheeted covering map of the bouquet of $n$ circles not possible?

1 vote
1 answer
79 views

Show that $Z=\{T\in\operatorname{Hom}(V, V)|T(\alpha)=0,\ \forall\alpha\in W\}$ is a subspace of $\operatorname{Hom}(V, V)$ and compute its dimension.

1 vote
1 answer
78 views

Show that $T_{i-1}\circ d_i =d_i^\prime\circ T_i$ for $\{T_i\}$, a Chain Map from $C$ to $C'$.

1 vote
2 answers
53 views

How to construct an unbounded set $A$ with outer measure $m^*(A)=3 ?$

1 vote
0 answers
106 views

Advanced Linear Algebra textbook complementing the contents & exercises of Brown's Book

1 vote
1 answer
50 views

An example of a sequence of rational numbers converging to an irrational number using the $\varepsilon-N$ definition.

0 votes
1 answer
53 views

How to visualize these quotient spaces of $\mathbb{\overline{B}}^2$ and $I\times I$?

0 votes
1 answer
67 views

Why is $\bar{\mathbb B}^n/\mathbb S^{n-1}$ homeomorphic to $\mathbb S^n$ and how to visualize a quotient map making the same identifications?

0 votes
0 answers
119 views

Book suggestions to learn more about Euler-Mascheroni constant

0 votes
0 answers
73 views

If $T^3=T$ show that $V=V_0\oplus V_1\oplus V_2$ , where the $V_i$ are subspaces of $V$ with some special properties.

0 votes
2 answers
42 views

Showing $\hom_{F}\left(\prod_{i=1}^{n}V_i\ ,\prod_{j=1}^{m}W_j\right)\cong\prod_{i=1}^{n}\prod_{j=1}^{m}\hom_{F}(V_i,W_j)$.

0 votes
1 answer
62 views

Proving $(V/\ker T)\cong F$ if $T:V\to F$ is a non-zero homomorphism.

0 votes
1 answer
122 views

If $\gamma$ is a smooth complex-valued function, then why is it uniformly continuous?

0 votes
1 answer
141 views

How to interpret the Maximum Modulus Principle for non-constant polynomials?

0 votes
0 answers
67 views

Visualizing Conway's definition of a Triangular path in his proof of Morera's Theorem