Keep undecided or unscheduled, as in We don't know how much fabric will be needed; let's leave that open, or The doctor leaves Fridays open for consultation. This expression uses open in the sense of “undetermined,” a usage dating from the mid-1500s.
leave oneself open. Remain vulnerable to; also, remain willing to consider. For example, Her actions left her open to widespread criticism, or I left myself open to further suggestions about how to proceed. Also see under lay open.