A Sheaf of Boehmians

TL;DR

This paper demonstrates that Boehmians over open sets in Euclidean space form a sheaf, satisfying the gluing property, thus providing a new sheaf-theoretic perspective on Boehmians.

Contribution

It establishes that Boehmians on open sets of ^N form a sheaf, highlighting their local-to-global compatibility in a sheaf-theoretic framework.

Findings

Boehmians satisfy the sheaf axioms over ^N.

The gluing property holds for Boehmians on open sets.

Boehmians can be viewed as a sheaf in the topological space ^N.

Abstract

We show that Boehmians defined over open sets of $\mathbb{R}^N$ constitute a sheaf. In particular, it is shown that such Boehmians satisfy the gluing property of sheaves over a topological space.