An italian real analysis book frequently uses the following definitions
Definition 1. Separated sets, separation elements.
The sets $A,B\subset\mathbb{R}$ are said to be separated if $a\leq b\quad\forall a\in A, \forall b\in B.$ It is said a separation element every $\lambda\in\mathbb{R}$ such that $a\leq\lambda\leq b\quad\forall a\in A, \forall b\in B.$
and
Definition 2. Adjacent sets.
The separated sets $A,B$ are said to be adjacent if they have a unique separation element.
These definitions are used, for example, to introduce the Riemann integral as the unique separation element between the sets of the inferior integral sums and the superior integral sums, when it exists.
My question is that I cannot be able to find such definitions on English language Wikipedia, so I would to know if they are used and under which names they go.