Baire's category theorem

Baire's category theorem

[¦berz ′kad·ə‚gȯr·ē ‚thir·əm]
(mathematics)
The theorem that a complete metric space is of second category; equivalently, the intersection of any sequence of open dense sets in a complete metric space is dense.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.