Search results with tag "State the baire category theorem"

The Baire category theorem - UCL

We are now ready to state the Baire category theorem: Theorem 7.3 (Baire category theorem) Let X be a complete metric space. Then: (a) A meager set has empty interior. (b) The complement of a meager set is dense. (That is, a residual set is dense.) (c) A countable intersection of dense open sets is dense.

  States, Category, Space, Theorem, Rabies, Countable, The baire category theorem, State the baire category theorem