The lattice of closed congruences on a topological lattice

Author:
Dennis J. Clinkenbeard

Journal:
Trans. Amer. Math. Soc. **263** (1981), 457-467

MSC:
Primary 06B30

DOI:
https://doi.org/10.1090/S0002-9947-1981-0594419-9

MathSciNet review:
594419

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Abstract: Our primary objectives are: (1) if is a lattice endowed with a topology making both the meet and join continuous then (i) the natural map which associates a congruence with the smallest topologically closed congruence containing it preserves finite meets and arbitrary joins; (ii) the lattice of such closed congruences is a complete Brouwerian lattice; (2) if is a topological (semi) lattice with the unit interval as a (semi) lattice homomorphic image then the lattice of closed (semi) lattice congruences has no compatible Hausdorff topology.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1981-0594419-9

Keywords:
Brouwerian lattice,
congruence lattice,
compact Hausdorff topological lattice

Article copyright:
© Copyright 1981
American Mathematical Society