EDB — 07F

[07F] Prerequisites:[07C]↺↻,[07D]↺↻,[252]↺↻.

Let \(\mathcal F\) be a non-empty family of intervals.

Show that the intersection \(\underline⋂{\mathcal F}\) of all intervals is an interval.

Suppose the intersection \(\underline⋂{\mathcal F}\) is not empty, show that the union \(\underline⋃{\mathcal F}\) is an interval.