Formal extension of the Whitney functor and duality

TL;DR

This paper introduces formal and polynomial extensions of certain cohomology functors and establishes a natural topological duality between them, advancing the theoretical framework in this area.

Contribution

It presents the first formal extension of the Whitney functor and the polynomial extension of the tempered cohomology functor, along with a duality theorem linking them.

Findings

Established a topological duality between the extended functors.

Defined new formal and polynomial extensions of cohomology functors.

Abstract

We introduce the formal extension of the Whitney functor and the polynomial extension of the tempered cohomology functor, and prove a natural topological duality between them.