Mousethief, no [patiently].... but a landlord can designate a unit as "no cats allowed" and then offer those apartments he can say have been pet-free as BEING pet free.
Look, I'm not just fooling around here to spout off for fun-- I've been a tenant all my life, a tenants-rights activist, a neighborhood activist, and we (I) held the Mudcat Dorm totally non-allergenic for about 5 years till no allergen-free-Mudcatters came. It CAN be done, but it requires thought and discipline.
It's not just about not letting critters into a space-- there are HVAC and nat'l airflow considerations as well.
If one expects a landlord to take that degree of trouble, it's a "bump" in rent to pay for that feature-- not a war with pet owners who have no issues. The pet owners are not out to get you, you know, they're just like you-- living their lives, their way.
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Gnu, in California, no-- a landlord cannot do all that without a law, if there is a lease. The tenant has remedies at law.