Definition

Let $X$ be a set. We say that $\mathcal{K}\subseteq 2^{X}$ is a sequential covering class of $X$ if and only if 1. $$\emptyset\in\mathcal{K}$$ 2. $$\forall A\subseteq X,\ \exists(E_{k})_{k\ge 1}\subseteq \mathcal{K}:A\subseteq \cup_{k=1}^{\infty}E_{k}$$ ## Examples 1. $X=\mathbb{R},\,\mathcal{K}=\{ [a,b):a<b \}$ 2. $X=\mathbb{R}^{n},\, \mathcal{K}=\{ [a_{1},b_{1})\times\dots \times[a_{n},b_{n}),a_{1}<b_{1},\dots,a_{n}<b_{n} \}$