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Connectedness Properties of Lattices

Published online by Cambridge University Press:  20 November 2018

R. Vainio*
Affiliation:
Department of MathematicsÅbo Akademi SF-20500 Åbo 50, Finland
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Abstract

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Let L be a lattice and q a convergence structure (or a topology) finer than the interval topology of L. In case of compact maximal chains and continuous lattice translations, the connected components of the space (L,q) are characterized using lattice conditions only. Moreover, lattice conditions of L are related to connectedness conditions of the order convergence space (L, o). Throughout this note, maximal chain conditions and maximal chain techniques play an important role.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1986

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