The concepts of L-fuzzy ideal generated by a L-fuzzy subset, L-fuzzy prime and completely prime ideal where L is a complete lattice are considered and some results are proved

In categories related to complete quasi-monoidal lattices, we investigate the relations among (L,♦)-(respectively, (L, )-,(L, )-) fuzzy quasi-uniform spaces, (L, ,∧)-fuzzy topological spaces and (L, ,∧)fuzzy interior spaces induced functions. Mathematics Subject Classification: 54A40, 08A72, 06D72

A poset game is a two-player game played over a partially ordered set (poset) in which the players alternate choosing an element of the poset, removing it and all elements greater than it. The first player unable to select an element of the poset loses. Polynomial time algorithms exist for certain restricted classes of poset games, such as the game of Nim. However, until recently the complexity...

We discuss some properties of a subposet of the Tamari lattice introduced by Pallo (1986), which we call the comb poset. We show that three binary functions that are not well-behaved in the Tamari lattice are remarkably well-behaved within an interval of the comb poset: rotation distance, meets and joins, and the common parse words function for a pair of trees. We relate this poset to a partial...

In this paper, we show that the dimension of the adjacency poset of a planar graph is at most 8. From below, we show that there is a planar graph whose adjacency poset has dimension 5. We then show that the dimension of the adjacency poset of an outerplanar graph is at most 5. From below, we show that there is an outerplanar graph whose adjacency poset has dimension 4. We also show that the dim...

In the first part of this article we present a realization of the m-Tamari lattice T (m) n in terms of m-tuples of Dyck paths of height n, equipped with componentwise rotation order. For that, we define the m-cover poset P〈m〉 of an arbitrary bounded poset P , and show that the smallest lattice completion of the m-cover poset of the Tamari lattice Tn is isomorphic to the m-Tamari lattice T (m) n...

The aim of this paper is to introduce two new types of fuzzy integrals, namely, ⊗-fuzzy integral and →-fuzzy integral, where ⊗ and → are the multiplication and residuum of a complete residuated lattice, respectively. The first integral is based on a fuzzy measure of L-fuzzy sets and the second one on a complementary fuzzy measure of L-fuzzy sets, where L is a complete residuated lattice. Some o...

In J. T. Wilson’s doctoral dissertation, the author takes up the subject of free meets, that is, subsets S of a frame L whose meet V S is preserved by a designated class of frame homomorphisms out of L. Wilson proves that all subsets of L have free meets if and only if the dual frame law holds in L and the assembly NL is a boolean frame. In this paper it is shown that a frame L has free meets w...

We prove that a globally hyperbolic spacetime with its causality relation is a bicontinuous poset whose interval topology is the manifold topology. This provides an abstract mathematical setting in which one can study causality independent of geometry and differentiable structure.

We consider a dichotomy for analytic families of trees stating that either there is a colouring of the nodes for which all but finitely many levels of every tree are nonhomogeneous, or else the family contains an uncountable antichain. This dichotomy implies that every nontrivial Souslin poset satisfying the countable chain condition adds a splitting real. We then reduce the dichotomy to a conj...