The general purpose of this paper is to prove quasiequilibrium existence theorems for production economies with general consumption sets in an infinite dimensional commodity space, without assuming any monotonicity of preferences or free-disposal in production.The commodity space is a vector lattice commodity space whose topological dual is a sublattice of its order dual. We formulate two kinds of properness concepts for agents' preferences and production sets, which reduce to more classical ones when the commodity space is locally convex and the consumption sets coincide with the positive cone. Assuming properness allows for extension theorems of quasiequilibrium prices obtained for the economy restricted to some order ideal of the commodity space. As an application, the existence of quasiequilibrium in the whole economy is proved without any assumption of monotonicity of preferences or free-disposal in production.

The aim of the paper is to provide a new proof of the Mas-ColellRichard existence of equilibrium result when preferences are non-transitive and incomplete. Our proof generalizes the main ideas of the Negishi approach to the case of unordered preferences.

The paper presents a survey of new results in general equilibrium theory with linear vector lattice commodity space (Kantorovich space). The importance of order structures and Riesz-Kantorovich formula is clarified. The main novelty of paper is new characterizations of fuzzy core elements in an exchange economy. Then these characterizations are applied to prove new quasiequilibrium existence theorem for linear vector lattice economy. This theorem, based on E-properness of preferences by Podczeck-Florenzano-Marakulin, develops Florenzano-Marakulin approach [14] and generalizes previous Tourky's results [27].