---- > [!theorem] Theorem. ([[the principle results of functional analysis (PROFA)]]) > Professor Rupflin calls the following results the **principle results of functional analysis (PROFA)**: > - [[Hahn-Banach Extension Theorem]] > - [[open mapping theorem]], which we prove here is equivalent to the > - [[open mapping theorem|bounded inverse theorem]] and > - [[closed graph theorem]] > - [[uniform boundedness principle]] > > An honorary mention goes to [[Baire category theorem|Baire's Theorem]] which, though a strictly [[topological space|topological]] result, is central to the proofs of all theorems above except [[Hahn-Banach Extension Theorem|Hahn-Banach]]. ---- #### ----- #### References > [!backlink] > ```dataview > TABLE rows.file.link as "Further Reading" > FROM [[]] > FLATTEN file.tags as Tag > WHERE Tag = "#definition" OR Tag = "#theorem" OR Tag = "#MOC" OR Tag = "#proposition" OR Tag = "#axiom" > GROUP BY Tag > ``` > [!frontlink] > ```dataview > TABLE rows.file.link as "Further Reading" > FROM outgoing([[]]) > FLATTEN file.tags as Tag > WHERE Tag = "#definition" OR Tag = "#theorem" OR Tag = "#MOC" OR Tag = "#proposition" OR Tag = "#axiom" > GROUP BY Tag > ```