If there is no written lease,  the rental is month to month; that means the tenancy could be terminated (ended) on 30 days notice. So while two people or business could not both lease the space at the same time, the landlord could lease the space to tenant 2 as long as the start date is after the termination of tenant's 1 tenancy, then give tenant 1 notice ending the tenancy. Thus, the space could be rented, for example, to a new tenant starting in a month while giving the current tenant his/her 30 days notice.