An uncountable Mittag-Leffler condition with an application to ultrametric locally convex vector spaces

TL;DR

This paper extends the Mittag-Leffler condition to uncountable index sets and applies it to prove an ultrametric analogue of a classical result, impacting the understanding of acyclicity in ultrametric locally convex spaces.

Contribution

It generalizes the Mittag-Leffler condition to uncountable sets and applies this to establish new results in ultrametric locally convex vector spaces.

Findings

Extended Mittag-Leffler condition to uncountable index sets.

Proved an ultrametric analogue of Palamodov's result.

Established acyclicity properties of ultrametric Fréchet spaces.

Abstract

Mittag-Leffler condition ensures the exactness of the inverse limit of short exact sequences indexed on a partially ordered set $(I,\leq)$ admitting a $countable$ cofinal subset. We extend Mittag-Leffler condition by relatively relaxing the countability assumption. As an application we prove an ultrametric analogous of a result of V.P.Palamodov in relation with the acyclicity of Frechet spaces with respect to the completion functor.