Search results with tag "The baire category theorem"
FUNCTIONAL ANALYSIS - ETH Z
people.math.ethz.chcloses with a proof of the Baire category theorem. Chapter 2 is devoted to the three fundamental principles of functional analysis. They are the Uniform Boundedness Principle (a pointwise bounded family of bounded linear operators on a Banach space is bounded), the Open Mapping Theorem (a surjective bounded linear operator between Banach
FUNCTIONAL ANALYSIS - People
people.math.ethz.chopen set. It closes with a proof of the Baire category theorem. Chapter 2 is devoted to the three fundamental principles of functional analysis. They are the Uniform Boundedness Principle (a pointwise bounded family of bounded linear operators on a Banach space is bounded), the Open Mapping Theorem (a surjective bounded linear operator between ...
The Baire category theorem - UCL
www.ucl.ac.ukTheorem 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.
The Baire category theorem - UCL
www.ucl.ac.ukMATHEMATICS 3103 (Functional Analysis) YEAR 2012–2013, TERM 2 HANDOUT #7: THE BAIRE CATEGORY THEOREM AND ITS CONSEQUENCES We shall begin this last section of the course by returning to the study of general metric