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 (joint with Dustin Clausen).