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Separating domains from algebraic domains

Xiaodong Jia, Qingguo Li, Wei Luan

Abstract

We prove that every domain that fails to be algebraic admits the unit interval $[0, 1]$ as its Scott-continuous retract. As a result, every countable domain is algebraic.

Separating domains from algebraic domains

Abstract

We prove that every domain that fails to be algebraic admits the unit interval as its Scott-continuous retract. As a result, every countable domain is algebraic.

Paper Structure

This paper contains 1 section, 2 theorems, 2 equations.

Table of Contents

  1. Acknowledgement

Key Result

Theorem 1

The unit interval $[0, 1]$ is a Scott-continuous retract of every domain that fails to be algebraic.

Theorems & Definitions (3)

  • Theorem
  • proof
  • Corollary