Intereting Posts

Do opposite categories always exist?
$4$ letter words taken from the letters of CONCENTRATIONS
Unambiguous terminology for domains, ranges, sources and targets.
Initial Segments of Modular Arithmetic
Can Someone approve the formula for the number of groups of order $p^2q$
Exist domains in complex plane with only trivial automorphisms?
Proof that sum of complex unit roots is zero
A result of Erdős on increasing multiplicative functions
Why abstract manifolds?
What is the next “Tribonacci-like” pseudoprime?
Split exact sequences
How to get a reflection vector?
Maps in $\mathbb{R}^n$ preserving harmonic functions
Notation on proving injectivity of a function $f:A^{B\;\cup\; C}\to A^B\times A^C$
Recursive formula for the number of connected labelled graphs with n vertices and k edges

Let $G$ be an open subset of $\mathbb{C}$. Prove that $(\mathbb{C}\cup \{ \infty\})-G$ is connected if and only if every connected component of $G$ is simply connected.

- On different definitions of neighbourhood.
- Continuity based on restricted continuity of two subsets
- Characterisation of extreme mono- and epi- morphisms in category of topological spaces.
- Basic questions about $\mathbb{Z}^{\mathbb{N}}$ with the product topology
- Showing the metric $\rho=\frac{d}{d+1} $ induces the same toplogy as $d$
- Special biholomorphic mapping from $ \mathbb{C} \setminus \{z : z \le 0\}$ to the unit disk
- On the product of $\mathfrak c$-many separable spaces
- Link between a Dense subset and a Continuous mapping
- Is every suborder of $\mathbb{R}$ homeomorphic to some subspace of $\mathbb{R}$?
- Conformal Map from Vertical Strip to Unit Disc

If the connected open set $H \subset \mathbb C$ is not simply connected, there is a simple closed curve $C$ in $H$ that is not homotopic to a point in $H$. Therefore there must be points inside $C$ that is not in $H$. Such a point and $\infty$ are in different connected components of $({\mathbb C} \cup \{\infty\} – G$.

- $a,b,c$ are positive reals and distinct with $a^2+b^2 -ab=c^2$. Prove $(a-c)(b-c)<0$
- Any two disjoint open sets are the interior and exterior of some set
- Are there any distinct finite simple groups with the same order?
- Why can we always take the zero section of a vector bundle?
- Isomorphisms: preserve structure, operation, or order?
- Finding the inverse of $f(x) = x^3 + x$
- Proving that $f(x)$ is irreducible over $F(b)$ if and only if $g(x)$ is irreducible over $F(a)$
- About powers of irrational numbers
- How to find $\lim\limits_{n\rightarrow \infty}\frac{(\log n)^p}{n}$
- How many solutions does the equation $x_1 + x_2 + x_3 = 11$ have, where $x_1, x_2, x_3$ are nonnegative integers?
- Possible generalizations of $\sum_{k=1}^n \cos k$ being bounded
- Sum of square of function
- What is the best approach when things seem hopeless?
- Are X and |X| independent? where $f(x)=\exp(-|x|)/2$
- $e$ to 50 billion decimal places