Exercise 15

For each, decide if it is a set of isomorphism class representatives.

• $\{\hskip 1.00006pt\mathbb{C}^{k}\mid k\in\mathbb{N}\hskip 1.00006pt\}$

• $\{\hskip 1.00006pt\mathcal{P}_{k}\mid k\in\text{$\{\hskip 1.00006pt-1,0,1,\ldots\hskip 1.00006pt\}$}\hskip 1.00006pt\}$

• $\{\hskip 1.00006pt\mathcal{M}_{m\!\times\!n}\mid m,n\in\mathbb{N}\hskip 1.00006pt\}$