New posts in examples-counterexamples

Give examples of clopen (open and closed) sets

real-analysis general-topology metric-spaces examples-counterexamples

Differentiable bijection $f:\mathbb{R} \to \mathbb{R}$ with nonzero derivative whose inverse is not differentiable

real-analysis examples-counterexamples inverse-function inverse-function-theorem

Continuity of the inverse $f^{-1}$ at $f(x)$ when $f$ is bijective and continuous at $x$.

real-analysis continuity examples-counterexamples inverse

Counterexample to the primality test

elementary-number-theory prime-numbers examples-counterexamples primality-test

Prove or disprove that ${F_{n}}^2 + 41$ is always a composite (if $F_{n}$ is $n^{th}$ Fibonacci number)

elementary-number-theory prime-numbers examples-counterexamples fibonacci-numbers

Double sequence, two sequences converge, but to different limits? [duplicate]

calculus real-analysis sequences-and-series convergence-divergence examples-counterexamples

A reflexive space which does not have an equivalent uniformly convex norm

functional-analysis reference-request banach-spaces examples-counterexamples

Example of similar matrices $A$ and $B$ such that products $AB$ and $BA$ are not similar

linear-algebra matrices examples-counterexamples

"Counterexample" for the Inverse function theorem

real-analysis examples-counterexamples inverse-function-theorem

Almost A Vector Bundle

differential-geometry examples-counterexamples vector-bundles

Is there a decreasing sequence of sets in $\mathbb{R}^{n}$ with these outer-measure properties?

real-analysis measure-theory lebesgue-measure examples-counterexamples outer-measure

Example of finitely generated subgroups whose intersection is not finitely generated

group-theory examples-counterexamples

Humorous integration example?

calculus integration soft-question examples-counterexamples

Do "exotic vectorfields" exist?

differential-geometry examples-counterexamples

Examples of subgroups where it's nontrivial to show closure under multiplication?

abstract-algebra group-theory examples-counterexamples big-list

What was Klein working on when he "replaces his Riemann surface by a metallic surface"?

reference-request soft-question intuition math-history examples-counterexamples

Example where Tietze Extension fails?

general-topology examples-counterexamples

In which topologies do open sets maintain open under countable or arbitrary intersection?

general-topology definition examples-counterexamples big-list

Example of Hausdorff space $X$ s.t. $C_b(X)$ does not separate points?

real-analysis general-topology examples-counterexamples separation-axioms

Is every countable space first countable?

general-topology examples-counterexamples