▾ Set of symbols
▾ Alphabet
▾ Deduction system
▾ Theory
▾ Zermelo-Fraenkel set theory
▾ Set
▾ Binary cartesian set product
▾ Binary relation
▾ Binary endorelation
▾ Preordering relation
▾ Partial ordering relation
▾ Partially ordered set
▾ Interval
▾ Set of intervals
▾ J-interval
▾ N-interval
▾ Real N-interval
▾ Set of euclidean real intervals
Elementary euclidean real set
Formulation 0
Let $\mathbb{R}^N$ be a D5630: Set of euclidean real numbers such that
(i) $\mathcal{P}_{\text{interval}}(\mathbb{R}^N)$ is the D3037: Set of euclidean real intervals in $\mathbb{R}^N$
A D11: Set $E \subseteq \mathbb{R}^N$ is an elementary euclidean real set in $\mathbb{R}^N$ if and only if \begin{equation} \exists \, I_1, \ldots, I_N \in \mathcal{P}_{\text{interval}}(\mathbb{R}) : E = \bigcup_{n = 1}^N I_n \end{equation}