My question involves landlord-tenant law in the State of: Tennessee
I am renting out a house, which is divided up as an apartment to 3 separate tenants. Everybody's lease clearly states the area exclusively rented to each tenant, and in addition there is a "common area" (accessible to ALL tenants) in the basement which contains laundry facilities and a kitchenette for the use of the 2 downstairs tenants. No one tenant is granted any more rights than any other tenant outside of their agreed rented area. All tenants can have company without notifying any of the other tenants, as in any apartment arrangement.
There was initially an issue with the upstairs tenant (renting the largest area) - they were not keeping the cat indoors per the pet agreement. They then declared that I (as landlord/manager) do NOT have any right to enter the property or "common area" without notifying them in advance first (thereby making enforcement of their cat staying "indoors" impossible). They sent me legal excerpts (TCA 66‑28‑513) that only address the issue of the landlord entering the exclusively rented private property of the tenant, which I don't believe applies to a common area if I'm not mistaken.
The issue to me is not the cat, but the fact that I continually am required to visit one of the other tenants in a common area to collect rent in partial payments - sometimes the other tenant is home, and other times he is not home and tells me he'll just leave the money somewhere in the common area.
As the apartment manager, am I required by law to notify this upstairs tenant each time I enter the DOWNSTAIRS common area to visit the other tenants (which is not part of the exclusively rented space?)
i.e. are aparment managers required to notify ALL tenants who want to be notified when the manager enters any COMMON area?

