 Positively separated sets

In mathematics, two non-empty subsets "A" and "B" of a given metric space ("X", "d") are said to be positively separated if the infimum

For example, on the real line with the usual distance, the open intervals (0, 2) and (3, 4) are positively separated, while (3, 4) and (4, 5) are not.In two dimensions, the graph of "y" = 1/"x" for "x" > 0 and the "x"-axis are not positively separated.