List questions from definition

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For any $H\le G$, $\lvert G\rvert=n$, and $k\in\Bbb N,$ we have that $H=\{a^k \mid a\in H\}$. What does this mean?

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Showing that the topology on a disjoint union is indeed atopology.

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Proving that $g(x)=x|x|$ is differentiable at $0$

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Definition of $\mathscr{L}^p$ space: is the 1/p-th power necessary

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How can I determine all the matrix A 3x3 in R such as AB=BA for all B 3x3 in R (without determinants)

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A question about the definition of a strictly increasing function

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Tu's Introduction to Manifolds - Definition of map locally trivial of rank r

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Proposition 12.9 - Tu's Introduction to Manifolds

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What is the formal definition of 'string'?

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Question about the notion/definition of "isolated local minimizer".

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What is the definition of the $SU(3)$ group?

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Why define derivative for a function defined on an interval

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Determining the homotopy colimit of the following diagram.

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why is the Radian not unit-less?

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List Question

Dimension of a Subspace?

For any $H\le G$, $\lvert G\rvert=n$, and $k\in\Bbb N,$ we have that $H=\{a^k \mid a\in H\}$. What does this mean?

Showing that the topology on a disjoint union is indeed atopology.

Proving that $g(x)=x|x|$ is differentiable at $0$

Definition of $\mathscr{L}^p$ space: is the 1/p-th power necessary

How can I determine all the matrix A 3x3 in R such as AB=BA for all B 3x3 in R (without determinants)

A question about the definition of a strictly increasing function

Tu's Introduction to Manifolds - Definition of map locally trivial of rank r

Proposition 12.9 - Tu's Introduction to Manifolds

What is the formal definition of 'string'?

Question about the notion/definition of "isolated local minimizer".

What is the definition of the $SU(3)$ group?

Why define derivative for a function defined on an interval

Determining the homotopy colimit of the following diagram.

why is the Radian not unit-less?

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