A person who owns a fee simple interest in a unit in a multi-unit building together with a specified undivided percentage of all common elements would be the owner of a:

Condominium

Explanation:

A condominium also called condo, is a housing unit in a multi-unit building that is owned by an individual. The owner of the condominium retains sole title to the unit but possesses common property mutually with other owners of the unit and shares common property expenses with them. The difference between an apartment and a condominium is ownership, that means an apartment is basically rented and a condominium is owned. Condo owners receive a deed for their estate, just as if they were buying a house. The condominium owner own his unit in fee simple, which is the less restrictive form of legally recognized real estate ownership. The owner usually has the right to sell and use the unit just like owners of a separate home unless such use or sale is prohibited by covenants. Ownership of a condominium is different from that of detached house e. g. you may possess inner walls of your unit but may not own outer walls.