New posts in examples-counterexamples

Can a function have a positive derivative at a point but not be increasing/decreasing around that point?

real-analysis derivatives examples-counterexamples

What's the difference between Complex infinity and undefined?

complex-analysis recreational-mathematics examples-counterexamples infinity

Dini's continuity vs Holder continuity

analysis continuity examples-counterexamples holder-spaces

pointwise convergence but not L1 convergence

real-analysis examples-counterexamples

Does continuity of $f$ imply $f^{-1}(\bar A)\subset\overline{f^{-1}(A)}$?

general-topology metric-spaces proof-writing continuity examples-counterexamples

Lebesgue Measurable Set which is not a union of a Borel set and a subset of a null $F_\sigma$ set?

measure-theory lebesgue-measure examples-counterexamples descriptive-set-theory borel-sets

A continuous image of a second countable space which is not second countable.

general-topology examples-counterexamples

List of proofs of non-trivial theorems which were unnoticed to be wrong for at least a few years

reference-request soft-question math-history examples-counterexamples big-list

Compact topological space not having Countable Basis?

general-topology compactness examples-counterexamples product-space second-countable

Open set containing rationals but complement non-denumerable

real-analysis general-topology examples-counterexamples

Is every open, bounded and simply connected subset of $\mathbb{R}^n$ essentially a ball?

general-topology algebraic-topology examples-counterexamples

Compactness, Local Compactness, Completeness

metric-spaces examples-counterexamples compactness

Example of Converge in measure, but not converge point-wise a.e.?

real-analysis measure-theory convergence-divergence examples-counterexamples

Examples of metric spaces which are not normed linear spaces?

general-topology functional-analysis metric-spaces examples-counterexamples normed-spaces

Example solutions for PDE

partial-differential-equations examples-counterexamples

A function that is bounded and measurable but not Lebesgue integrable

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

Simple (even toy) examples for uses of Ordinals?

set-theory examples-counterexamples ordinals

Continuous Functions and Cauchy Sequences

real-analysis sequences-and-series continuity examples-counterexamples cauchy-sequences

Example for non-Riemann integrable functions

real-analysis integration riemannian-geometry examples-counterexamples

Tensor products over field do not commute with inverse limits?

linear-algebra examples-counterexamples tensor-products