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123 Answers

newest activity votes
22
Compute $\int \frac{\sin(x)}{\sin(x)+\cos(x)}\mathrm dx$
7
$AB-BA=I$ having no solutions
7
Is $e^x$ the only isomorphism between the groups $(\mathbb{R},+)$ and $(\mathbb{R}_{> 0},*)$?
6
Finding the number of eigenvector(s) of non-zero linear transformation $T$ to $R$
6
Basic group theory exercise
6
calculate $\int_{0}^{i} e^z\, dz$
5
Real Variable. Function.
5
Prove that a finite set of points $z_1,z_2,…,z_n$ cannot have any accumulation points.
5
Open mapping of the unit ball into itself
4
Solving a complex integral 1
4
$I-AB$ be invertible $\Leftrightarrow$ $I-BA$ is invertible
4
Properties of the set $\mathbb{R}$ with the metric $d(x ,y )=|x- y|/(1+|x-y|)$
4
Check whether sets are open, closed, compact or bounded
4
Continuous function on unit circle has fixed point
4
Finding $a$ from $\lim\limits_{x\rightarrow0}(1+a\sin x)^{\csc x} =4$
4
Proving $f(x)=x^2$ is uniformly continuous on $[0,b]$ for any $b\gt 0$.
3
Proving bounded entire functions
3
Continuous map between metric spaces
3
Homeomorphism between $\mathbb{R}_+ \times \mathbb{R}_+$ and $\mathbb{R}_+ \times \mathbb{R}$
3
The existence of a group automorphism with some properties implies commutativity.
3
What does $C[0,1]$ mean?
3
Two problems: When a countinuous bijection is a homeomorphism? Possible cardinalities of Hamel bases?
3
Does this proof that $2\mathbb{Z}\not\cong 3\mathbb{Z}$ work?
3
Algebraic Topology pamphlets?
3
Does there exist a function $f:[0,1] \to[0,1]$ such its graph is dense in $[0,1]\times[0,1]$?
3
study topology: homotopy and homology
3
Prove that for $n\ne -1$ $\frac{1}{2\pi i}\int_{C} z^ndz=0$
2
diagonalisability of matrix few properties
2
For any point $ a $ of a compact subset $ S $ of a metric space, prove that there exists a nearest point $ c $ to $ a $.
2
Number of Fixed Point(s) of a Differentiable Function
1 2 3 4 5