The half-open window let in a cool breeze that carried the scent of rain.

The half-open interval [0, 1) contains 0 but not 1, so it is neither open nor closed in the usual topology on R.

Controlling the half-open file allowed White to invade Black's position with rooks.

The forensic analyst discovered multiple half-open files on the compromised workstation, suggesting interrupted uploads.

When plotting the solution set, make sure to mark the endpoints of the half-open intervals clearly.