Finite Intervals in the Lattice of Topologies

W. R. Brian*, Christopher Good, R. W. Knight, D. W. McIntyre

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We prove a conjecture of Reinhold: that a finite lattice is isomorphic to an interval in the lattice of topologies on some set if and only if it is isomorphic to an interval in the lattice of topologies on a finite set.

Original languageEnglish
Pages (from-to)325-335
Number of pages11
JournalOrder
Volume31
Issue number3
Early online date20 Sept 2014
DOIs
Publication statusPublished - Nov 2014

Keywords

  • Finite intervals of topologies
  • Finite topologies
  • Lattice of topologies
  • Quasiorders

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Geometry and Topology
  • Computational Theory and Mathematics

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