On compactness of lattices (Q2368373)

The author studies topology-like compactness and normality properties of lattices through measurability techniques. Special cases include such notions as countable compactness, almost countable compactness and countable paracompactness. The investigated properties either relate to a single lattice \(\mathbf{L}\) (or to a pair of lattices \(\mathbf{L_1}\subset \mathbf{L_2}\)) of subsets of a nonempty set \(\mathbf{X}.\) The study makes use of various subsets of \(\mathbf{I}(\mathbf{L}),\) the set of non-trivial zero-one-valued, finitely additive measures on \(\mathbf{A}(\mathbf{L})\), where \(\mathbf{A}(\mathbf{L})\) denotes the algebra generated by \(\mathbf{L}.\)