(referring to an interval on the real line) containing only one of its endpoints(adjective)
Wiktionary.org : Text is available under the Creative Commons Attribution-ShareAlike License
Use "half-open" in a sentence
"By matching the colored sphere on the left side with the ones on the right side, the user swaps between the four modes: open, half-open, closed and graph."
"Something creaked outside the half-open door, and he jumped."
"When I returned my gaze to Sebastian, his eyes were half-open and fixed on me in a quiet, unreadable way."