What determines when the tenant relinquishes tenancy?

[Chris Hertig]

Hello all!  We had a tenant who gave us notice she was leaving (September 30th).  She paid through the end of the month, and was moving out of state.  In her written notice, she stated she would be out "...no later than the 19th..." On the 25th, I went to check on the status - the door was wide open (literally!), the place was completely empty, and the keys were left on the kitchen counter.   Wouldn't this all equate to her relinquishing her tenancy, even though it is a couple days before the end of the month?  She claims the place was still hers until the end of the month, even though nothing was there and she was no longer in the state?