On continuous noncomplete lattices

K. V. Adaricheva, V. A. Gorbunov, M. V. Semenova

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

We consider noncomplete continuous and algebraic lattices and prove that finitely generated free lattices are algebraic. We also study the Lawson topology, the second most important topology in the theory of continuous domains, on finitely presented lattices. In particular, we prove that algebraic finitely presented lattices are linked bicontinuous and the Lawson topology on these lattices coincides with the interval topology. Several examples of non-distributive and noncomplete algebraic and continuous lattices are given in the paper.

Original languageEnglish
Pages (from-to)215-230
Number of pages16
JournalAlgebra Universalis
Volume46
Issue number1-2
Publication statusPublished - 2001
Externally publishedYes

Fingerprint

Continuous Lattice
Algebraic Lattice
Topology
Finitely Generated
Interval

Keywords

  • Continuous
  • Finitely presented
  • Interval topology
  • Lattice
  • Lawson topology

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

Adaricheva, K. V., Gorbunov, V. A., & Semenova, M. V. (2001). On continuous noncomplete lattices. Algebra Universalis, 46(1-2), 215-230.

On continuous noncomplete lattices. / Adaricheva, K. V.; Gorbunov, V. A.; Semenova, M. V.

In: Algebra Universalis, Vol. 46, No. 1-2, 2001, p. 215-230.

Research output: Contribution to journalArticle

Adaricheva, KV, Gorbunov, VA & Semenova, MV 2001, 'On continuous noncomplete lattices', Algebra Universalis, vol. 46, no. 1-2, pp. 215-230.
Adaricheva KV, Gorbunov VA, Semenova MV. On continuous noncomplete lattices. Algebra Universalis. 2001;46(1-2):215-230.
Adaricheva, K. V. ; Gorbunov, V. A. ; Semenova, M. V. / On continuous noncomplete lattices. In: Algebra Universalis. 2001 ; Vol. 46, No. 1-2. pp. 215-230.
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