New posts in examples-counterexamples

$f$ bounded but $f'$ isn't

Can the product of three complex numbers ever be real?

What's so cool about local compactness?

What are some examples of hard theorems in category theory?

Examples of closed subspaces of Baire spaces that fail to be Baire?

Weird subfields of $\Bbb{R}$

Hausdorff Quasi-Polish spaces

An example of a space which fails to be compactly generated

Nonpiecewise Function Defined at a Point but Not Continuous There

Is there a group $G$ and subgroup $H$, such that there exists $g\in G$ with $gHg^{-1} \subset H$ and $|H:gHg^{-1}|$ is infinite?

Is the property "being a derivative" preserved under multiplication and composition?

Example of a Markov chain transition matrix that is not diagonalizable?

Example of non-homeomorphic compact spaces $K_1$ and $K_2$ such that $K_1\oplus K_1$ is homeomorphic to $K_2\oplus K_2$

Function in $H^1$, but not continuous

Topology on $\mathbb{R}$ strictly coarser (resp. finer) than the usual one which is still Hausdorff (resp. connected)

Easy to understand examples of category theoretic theorems that are useful

Famous uses of the inclusion-exclusion principle?

A free submodule of a free module having greater rank the submodule

Looking for a counter example for non-connected intersection of descending chain of closed connected sets

Nonhomeomorphic subsets of the plane