New posts in examples-counterexamples

Does $f$ have a critical point if $f(x, y) \to +\infty$ on all horizontal lines and $f(x, y) \to -\infty$ on all vertical lines?

Example of Intersection of Pure Subgroup which is not Pure

Counterexample for the Open Mapping Theorem

Can intersection of two manifolds be $xy=0$

Examples of comma categories

$X = [0,1]^{[0,1]}$ with different topologies [closed]

Integrability: Neither improper Riemann nor Lebesgue but Henstock-Kurzweil

Every minimal Hausdorff space is H-closed

Is $\mathbb{C}^*$ modulo the roots of unity isomorphic to $\mathbb{R}^+$?

Homeomorphism between Space and Product: $X \cong X \times X$

Example of topological spaces where sequential continuity does not imply continuity

give a counterexample of monoid

Can monics always be "made left-invertible" by adding arrows?

Example of an uncountable dense set with measure zero

Does an abelian subgroup inject into the abelianisation of the whole group? [closed]

Examples of bounded linear operators with range not closed

Cantor curve is not absolutely continuous

Examples for proof of geometric vs. algebraic multiplicity

Difference between being faithful and being injective on arrows

Connected and Compact preserving function is not continuous example?