New posts in examples-counterexamples

Motivation and examples for ramification

Example of a continuous function with a discontinuous inverse

If $V \times W$ with the product norm is complete, must $V$ and $W$ be complete?

If $S \subseteq X$ is closed, is $f(S,r)$ necessarily closed?

Does $\{f_ng_n\}\to fg$ uniformly?

A countale partially ordered set that has an uncountable number of maximal chains

Does $S^\bot+T^\bot = (S\cap T)^\bot$ hold in infinite-dimensional spaces?

Give an example of a simply ordered set without the least upper bound property.

Does separability imply the Lindelöf property?

Is a product of derivatives still a derivative? [duplicate]

A strong Hausdorff condition

Find $f:C\to\mathbb{R}^2$ continuous and bijective but not open, $C\subset\mathbb{R} ^2$ is closed and connected

A congruence with the Euler's totient function and sum of divisors function

Examples of bi-implications ($\Leftrightarrow$) where the $\Rightarrow$ direction is used in the proof of the $\Leftarrow$ direction.

If $R[x]$ and $R[[x]]$ are isomorphic, then are they isomorphic to $R$ as well? [duplicate]

Infinite series involving $\sqrt{n}$

Is there a field extension $K / \Bbb Q$ such that $\text{Aut}_{\Bbb Q}(K) \cong \Bbb Z$?

Countably generated sigma-algebras

A locally injective but non globally injective function?

Limit point Compactness does not imply compactness counter-example