1. <programming> To prepare to read or write a file. This usually involves checking whether the file already exists and that the user has the necessary authorisation to read or write it. The result of a successful open is usually some kind of capability (e.g. a Unix file descriptor) - a token that the user passes back to the system in order to access the file without further checks and finally to close the file.
2. <character> Abbreviation for "open (or left) parenthesis" - used when necessary to eliminate oral ambiguity. To read aloud the LISP form (DEFUN FOO (X) (PLUS X 1)) one might say: "Open defun foo, open eks close, open, plus eks one, close close."
4. <mathematics> open interval.