Given a Hausdorff space X, we calculate the tightness and the character of the hyperspace CL∅(X) of X, endowed with either the co-compact or the lower Vietoris topology, and give some estimates for the tightness of CL∅(X), endowed with the Fell topology.\ud \ud Some properties related to first-countability and countable tightness, such as sequentiality, Fréchet property and, less directly, radiality and pseudoradiality, are investigated as well.\ud \ud To carry out our investigation, we also consider on the base space X several cardinal functions, and we compare some of them (which are newly defined or not so well known) with other classical ones, obtaining results and counterexamples which may be of some independent interest

We show that every quasi-metric space is isomorphic to a subspace of the hyperspace of a suitable metric space, endowed with the Hausdorff quasi-metric. Therefore a topological space is quasi-metrizable if and only if it can be embedded in a Hausdorff quasi-metric hyperspac

We prove an algebraic and a topological decomposition theorem for complete D-lattices (i.e., lattice-ordered effect algebras). As a consequence, we obtain a HammerSobczyk type decomposition theorem for modular measures on D-lattices.

Let L be a lattice ordered effect algebra. We prove that the lattice uniformities on L which make uniformly continuous the operations and ⊕ of L are uniquely determined by their system of neighborhoods of 0 and form a distributive lattice. Moreover we prove that every such uniformity is generated by a family of weakly subadditive [0, +∞]-valued functions on L.

We prove a Carathéodory type extension theorem for