New posts in examples-counterexamples

An example of a non-paracompact topological space

If $f:[a,b]\to \mathbb{R}$ satisfies $|f'(x)|<1, \forall x\in [a,b]$, is $f$ necessarily a contraction?

Concrete examples of group actions.

What are some interesting counterexamples given by finite topological spaces?

Counterexample for graph isomorphism using eigenvalue multiplicity (connected graphs)

Two claims about compositorials

Pretty conjecture $x^{\left(\frac{y}{x}\right)^n}+y^{\left(\frac{x}{y}\right)^n}\leq 1$

Example of a function in $L^2(\mathbb{R})$ with derivative not in $L^2(\mathbb{R})$.

Is total boundedness a topological property?

Does the Laplace transform biject?

Why differentiability implies continuity, but continuity does not imply differentiability?

Extending Herstein's Challenging Exercise to Modules

sigmoid $\circ$ sigmoid = sigmoid?

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

Counterexample to Tonelli's theorem

Non-examples for the Kato-Rellich Theorem

Associative, non-commutative, nontrivial operation on the real numbers

Universal property characterizing $\Bbb R$

Does there exist a function $f: \mathbb{R} \to \mathbb{R}$ that is differentiable only at $0$ and at $\frac{1}{n}$, $n \in \mathbb{N}$?

Examples of bijections from $\mathbb Z\to\mathbb Z$ such that their sum is a bijection?