texas: month to month lease question

A few months ago after my 6 month lease was up, I went on a month to month lease with my apartment complex. The last few days of the month, I would just go in and tell them I needed another month. Around july 20 this month, a gentleman knocked on my door asking to view my apartment because he"s renting it. I explained that I lived there. And though I hadn't told the office yet, was staying till at least september 15th. I went to the office the next day, and they confirmed they rented it out. I thought it was the tenants responsibility to say they are moving out. Now the office is making me move to another unit. Can they do this? Thanks!

[AFFA]

I wish to inform you that in a month to month lease also termination can be done by giving notice of termination. The party which intends to terminate the lease will have to inform the other party. Therefore, either you or your landlord can give notice of termination of lease.

AFF