Adjective
partially open; ajar
(mathematics) (referring to an interval on the real line) containing only one of its endpoints
Source: en.wiktionary.orghalf open
Her curiosity was too much for her. She felt almost as if she could hear the books whispering on the other side of the half-open door. They were promising her a thousand unknown stories, a thousand doors into worlds she had never seen before. Cornelia Funke