Integration on differential spaces

TL;DR

This paper extends classical differential calculus concepts to differential spaces, introducing generalized structures like n-dimensional chains and forms, and establishing an analogue of Stokes theorem in this broader context.

Contribution

It introduces a framework for integration on differential spaces, generalizing classical differential geometry concepts and proving an analogue of Stokes theorem.

Findings

Defined n-dimensional chains and forms on differential spaces

Established an analogue of Stokes theorem for these spaces

Extended classical differential calculus to a broader setting

Abstract

The generalization of the n-dimensional cube, an n-dimensional chain, the exterior derivative and the integral of a differential n-form on it are introduced and investigated. The analogue of Stokes theorem for the differential space is given.