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

In: Mathematica Slovaca, vol. 66, no. 3
P. Douka - V. Felouzis

Details:

Year, pages: 2016, 545 - 556
Keywords:
lattices, linear ordered spaces, orderable topological spaces
About article:
We give necessary and sufficient conditions for a family $\mathcal{M}$ of subsets of a set $X$ which completely separates $X$ to be a sublattice of the lattice of $\mathscr{C}(X,≤)$ of all convex subsets of $X$, with respect to a suitable linear ordering $≤$ of $X$. As an application we give a characterization of Hausdorff topological spaces which are orderable or suborderable.
How to cite:
ISO 690:
Douka, P., Felouzis, V. 2016. Families of sets which can be represented as sublattices of the lattice of convex subsets of a linearly ordered set. In Mathematica Slovaca, vol. 66, no.3, pp. 545-556. 0139-9918. DOI: https://doi.org/10.1515/ms-2015-0156

APA:
Douka, P., Felouzis, V. (2016). Families of sets which can be represented as sublattices of the lattice of convex subsets of a linearly ordered set. Mathematica Slovaca, 66(3), 545-556. 0139-9918. DOI: https://doi.org/10.1515/ms-2015-0156
About edition:
Published: 1. 6. 2016