Newbetuts

Counterexamples for "every linear map on an infinite dimensional complex vector space has an eigenvalue"

Primality test for numbers of the form $(10^p-1)/9$ (and maybe $((10 \cdot 2^n)^p-1)/(10 \cdot 2^n-1)$)

Prove that $X_1\cup X_2$ is path connected if and only if both $X_1$ and $X_2$ are path connected

Examples of closed sets with empty interior

Sequentially closed $\implies$ closed, but not Fréchet-Urysohn space

Let $B$ be a countable set and let $f$ be a surjective function ($f:A\to B$), then $A$ is also countable

Can a space $X$ be homeomorphic to its twofold product with itself, $X \times X$?

Give an example of a non abelian group $G$ and a subgroup $H\subset Z(G) $(proper subgroup) such that $H$ is not characteristic subgroup of $G$

Why is a monoid with right identity and left inverse not necessarily a group? [duplicate]

Measure Spaces: Uniform & Integral Convergence

$\operatorname{Aut}(G)\cong \Bbb{Z}/8\Bbb{Z}$

convergence of sequence of averages the other way around

Lawvere theories with two generic objects

Find $f(x,y )$ such that $f_{x},f_{y},f_{yx}$ are continuous,but $f_{xy}$ is not

Is every contractible space a cone?

Example of a functor preserving only finite coproducts

I want an example of a sequence that satisfies $\mid x(n) - x(n-1)\mid \to 0$ but not Cauchy [duplicate]

New posts in examples-counterexamples

Is there an example for an undefinable number?

Counterexample for the normalizer being a normal subgroup

Applications of Eckmann–Hilton argument

Counterexamples for "every linear map on an infinite dimensional complex vector space has an eigenvalue"

Primality test for numbers of the form $(10^p-1)/9$ (and maybe $((10 \cdot 2^n)^p-1)/(10 \cdot 2^n-1)$)

Prove that $X_1\cup X_2$ is path connected if and only if both $X_1$ and $X_2$ are path connected

Examples of closed sets with empty interior

Sequentially closed $\implies$ closed, but not Fréchet-Urysohn space

Let $B$ be a countable set and let $f$ be a surjective function ($f:A\to B$), then $A$ is also countable

Can a space $X$ be homeomorphic to its twofold product with itself, $X \times X$?

Give an example of a non abelian group $G$ and a subgroup $H\subset Z(G) $(proper subgroup) such that $H$ is not characteristic subgroup of $G$

Why is a monoid with right identity and left inverse not necessarily a group? [duplicate]

Measure Spaces: Uniform & Integral Convergence

$\operatorname{Aut}(G)\cong \Bbb{Z}/8\Bbb{Z}$

convergence of sequence of averages the other way around

Lawvere theories with two generic objects

Find $f(x,y )$ such that $f_{x},f_{y},f_{yx}$ are continuous,but $f_{xy}$ is not

Is every contractible space a cone?

Example of a functor preserving only finite coproducts

I want an example of a sequence that satisfies $\mid x(n) - x(n-1)\mid \to 0$ but not Cauchy [duplicate]