Semicontinuity of the energy functional was essential to prove the existence of a minimizer.

The pump ran semicontinuously, supplying bursts of coolant during brief pauses in operation.

During the seminar, the mathematician introduced a semicontinuous function that is continuous almost everywhere but fails to be continuous at certain points where it becomes upper or lower semicontinuous.

On a compact space, any upper semicontinuous real-valued function attains its maximum.

To apply the direct method in the calculus of variations, we require that the energy functional be lower semicontinuous and coercive, which guarantees the existence of a minimizer.