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Egyptian fractions on groups

David A. Ross

Abstract

Results about the structure of the set of Egyptian fractions on the line are extended to subsets of topological groups.

Egyptian fractions on groups

Abstract

Results about the structure of the set of Egyptian fractions on the line are extended to subsets of topological groups.

Paper Structure

This paper contains 8 sections, 13 theorems, 11 equations.

Table of Contents

  1. Introduction
  2. Note on the proofs
  3. Statement of results
  4. Ultrapowers of groups
  5. Definitions
  6. Properties
  7. Comments
  8. Proofs

Key Result

Theorem 2.1

For $n>0$ the set $E'_n:=T'_1+\cdots+T'_n$ is compact (where $A'=A\cup\{0\}$)

Theorems & Definitions (24)

  • Example 2.1
  • Example 2.2
  • Theorem 2.1
  • Corollary 2.1
  • Corollary 2.2
  • proof : Proof of corollaries
  • Theorem 2.2
  • Theorem 2.3
  • Theorem 2.4
  • Theorem 2.5
  • ...and 14 more