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The sup-completion of a Dedekind complete vector lattice II

Youssef Azouzi, Youssef Nasri

Abstract

We persist in our investigation of the sup-completion of a Dedekind complete Riesz space, extending to the broader context of Riesz spaces. some results initially obtained by Feng, Li, Shen, and also by Erdös, and Rényi.

The sup-completion of a Dedekind complete vector lattice II

Abstract

We persist in our investigation of the sup-completion of a Dedekind complete Riesz space, extending to the broader context of Riesz spaces. some results initially obtained by Feng, Li, Shen, and also by Erdös, and Rényi.
Paper Structure (5 sections, 29 theorems, 138 equations)

This paper contains 5 sections, 29 theorems, 138 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. More about finite and infinite parts
  4. The star map
  5. Applications

Key Result

Lemma 1

Let $\left( x_{\alpha}\right) ,\left( y_{\alpha}\right)$ be two nets in $X_{+}^{s}$ such that $\left( x_{\alpha}\right) \perp\left( y_{\alpha}\right) .$ Then the following statements hold.

Theorems & Definitions (36)

  • Lemma 1
  • Lemma 2
  • Lemma 3
  • Remark 4
  • Remark 5
  • Lemma 6
  • Remark 7
  • Remark 8
  • Proposition 9
  • Proposition 10
  • ...and 26 more