New posts in Examples Counterexamples

Examples of almost compact spaces.

handshaking lemma and Erdos-Gallai theorem

Counterexample regarding basic properties of limits

Homeomorphic metric spaces where the identity map is not a homeomorphism

A category which direct limits but no general colimits

Functor that does not preserve monic and epic

$n$ is prime iff $\binom{n^2}{n} \equiv n \pmod{n^4}$?

Given that $x_0$ is a real root of $x^3+px + q = 0$, how can I show that $p^2 \geq 4x_0q$?

How big can $U\subset\mathbb{C}$ be if there exists a non-constant holomorphic $f\colon U\to\mathbb{C}$ with $2f(2z)=f(z)+f(z+1)?$

Functions $f: \mathbb{Z}^{+}\to \mathbb{R}$ satisfying $x f(y) + y f(x) = (x+y) f(x^2+y^2)$