Category Phenomena

  • Chuanming Zong
  • James J. Dudziak
Part of the Universitext book series (UTX)


In a metric space {ℜ, ρ}, a subset is called meager or of the first category if it can be represented as a countable union of nowhere dense subsets. We say that a property holds for most1 elements of Ii if it holds for all elements of ℜ that lie off a meager subset. In 1899, R. Baire [1] found that every meager subset of a compact metric space or a locally compact metric space has a dense complement. So, in a topological sense, meager sets are “small,” whereas their complements are “large.”


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Copyright information

© Springer-Verlag New York, Inc. 1996

Authors and Affiliations

  • Chuanming Zong
    • 1
  • James J. Dudziak
    • 2
  1. 1.Institute of MathematicsThe Chinese Academy of SciencesBeijingPR China
  2. 2.Department of MathematicsBucknell UniversityLewisburgUSA

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