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Mathematica Slovaca

Editor-in-Chief: Pulmannová, Sylvia


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Volume 66, Issue 3

Issues

Families of sets which can be represented as sublattices of the lattice of convex subsets of a linearly ordered set

P. Douka / V. Felouzis
Published Online: 2016-08-17 | DOI: https://doi.org/10.1515/ms-2015-0156

Abstract

We give necessary and sufficient conditions for a family M of subsets of a set X which completely separates X to be a sublattice of the lattice of C(X,) of all convex subsets of X, with respect a suitable linear ordering ≤ of X. As an application we give a characterization of Hausdorff topological spaces which are orderable or suborderable.

MSC 2010: Primary 06B15; Secondary 06B30, 54F05

Keywords: lattices; linear ordered spaces; orderable topological spaces

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About the article


Received: 2013-04-24

Accepted: 2013-12-13

Published Online: 2016-08-17

Published in Print: 2016-06-01


Citation Information: Mathematica Slovaca, Volume 66, Issue 3, Pages 545–556, ISSN (Online) 1337-2211, ISSN (Print) 0139-9918, DOI: https://doi.org/10.1515/ms-2015-0156.

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