The Big Three Pt. 6 - Closed Graph Theorem with Applications
(Before everything: elementary background in topology and vector spaces, in particular Banach spaces, is assumed.) A surprisi...
The Big Three Pt. 5 - The Hahn-Banach Theorem (Dominated Extension)
About this postThe Hahn-Banach theorem has been a central tool for functional analysis and therefore enjoys a wide variety, m...
The Big Three Pt. 4 - The Open Mapping Theorem (F-Space)
The Open Mapping TheoremWe are finally going to prove the open mapping theorem in $F$-space. In this version, only metric and...
The Big Three Pt. 3 - The Open Mapping Theorem (Banach Space)
What is open mappingAn open map is a function between two topological spaces that maps open sets to open sets. Precisely spea...
The Big Three Pt. 2 - The Banach-Steinhaus Theorem
About this blog postPeople call the Banach-Steinhaus theorem the first of the big three, which sits at the foundation of line...
The Big Three Pt. 1 - Baire Category Theorem Explained
About the ‘Big Three’There are three theorems about Banach spaces that occur frequently in the crux of functional analysis, w...