| 释义 |
Baire Category Theorem The theorem involves two statements, neither of which implies the other. (i) Every complete metric space is a Baire space. (ii) Every locally compact Hausdorff space is a Baire space. The theorem has many important applications in functional analysis, including implying an algebraic (or Hamel) basis of an infinite-dimensional Banach space must be uncountable and so motivating the need for Schauder bases.
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