Abstract: In this paper, the author establishs general open mapping theorems for continuous, weakly continuous, closed and weakly singular linear maps respectively. From these general theorems, he deduces a lot of specific open mapping theorems. which include some well-known theorems and some new interesting results. Particularly the author gives the extensions of Husain's open mapping theorem and Adasch's open mapping theorem.

Key words: Locally convex spaces, duals, barrelled spaces, Mackey spaces, open mapping theorems