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

Rok, strany: 2016, 545 - 556

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.

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