The duality between lattice-ordered monoids and ordered topological spaces
type: Item
instance of: scholarly article
title: The duality between lattice-ordered monoids and ordered topological spaces
zbMATH Open document ID: 0599.54041
DOI: 10.1007/BF02573322
published in: Semigroup Forum
publication date: 1984-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/134679
review text: The authors show that a realcompact ordered space X can be characterized by the lattice-ordered convergence monoid \(C(X,{\mathbb{R}}^+)\) of continuous isotone functions on X to the non-negative reals \({\mathbb{R}}^+\), and that a zero-dimensionally realcompact ordered space X can be determined by the lattice-ordered convergence monoid C(X,\({\mathbb{N}})\) of continuous isotone functions on X to the natural numbers \({\mathbb{N}}\) if the order is discrete, chain or Dedekind complete.
Mathematics Subject Classification ID: 54F05
Mathematics Subject Classification ID: 54D60
Mathematics Subject Classification ID: 06F30
Mathematics Subject Classification ID: 54B30
Mathematics Subject Classification ID: 06F05
zbMATH DE Number: 3967426
zbMATH Keywords: (zero-dimensionally) realcompact ordered space
zbMATH Keywords: discrete order
zbMATH Keywords: chain complete order
zbMATH Keywords: Dedekind complete order
zbMATH Keywords: lattice-ordered convergence monoid
author: Tae Ho Choe
author: S. S. Hong
MaRDI profile type: Publication
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cites work: Applications of the Theory of Boolean Rings to General Topology
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description: scientific article; zbMATH DE number 3967426