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A Sheaf of Boehmians

Jonathan Beardsley, Piotr Mikusinski

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.

A Sheaf of Boehmians

Abstract

We show that Boehmians defined over open sets of constitute a sheaf. In particular, it is shown that such Boehmians satisfy the gluing property of sheaves over a topological space.

Paper Structure

This paper contains 6 sections, 27 theorems, 18 equations.

Table of Contents

  1. INTRODUCTION
  2. PRELIMINARIES
  3. BOEHMIANS ON OPEN SETS
  4. A GLUING PROPERTY
  5. A SHEAF OF BOEHMIANS
  6. Fundamental and Cauchy sequences

Key Result

Lemma 1

If $K\Subset\mathbb{R}^N$, $f\in\mathscr{C}({K})$, $\varphi\in\mathscr{D}$, and $s(\varphi)<\varepsilon$, then

Theorems & Definitions (52)

  • Lemma 1
  • Corollary 1
  • Theorem 1
  • proof
  • Lemma 2
  • proof
  • Corollary 2
  • proof
  • Definition 1
  • Lemma 3
  • ...and 42 more