Also appears in collection : Fields medallists - 2018
(joint with Dustin Clausen) Based on the condensed formalism, we propose new foundations for real functional analysis, replacing complete locally convex vector spaces with a variant of so-called p-liquid condensed real vector spaces, with excellent categorical properties; in particular they form an abelian category stable under extensions. It is a classical phenomenon that local convexity is not stable under extensions, so one has to allow non-convex spaces in the theory, and p-liquidity is related to p-convexity, where 0 inferior at p inferior or equal at1 is an auxiliary parameter. Strangely, the proof that the theory of p-liquid vector spaces has the desired good properties proceeds by proving a generalization over a ring of arithmetic Laurent series.
By Dustin Clausen
By Riccardo Zanfa
By Jean-Claude Belfiore
By Daniel Bennequin
By Samson Abramsky
By Jens Hemelaer
By Francesco Genovese
By Vasudevan Srinivas
By Marc Levine
