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 for algebraic frames L wit...

In this paper, Lowen’s strong fuzzy compactness and ultra-fuzzy compactness of I -topological spaces are extended to L-subsets, for L—a complete lattice. The properties of strong fuzzy compact L-subsets and ultra-fuzzy compact L-subsets are studied in detail here, and comparisons between these notions as well as the notion of N-compactness are shown. c © 2004 Elsevier B.V. All rights reserved.

Spleen is known to contain multiple dendritic and myeloid cell subsets, distinguishable on the basis of phenotype, function and anatomical location. As a result of recent intensive flow cytometric analyses, splenic dendritic cell (DC) subsets are now better characterized than other myeloid subsets. In order to identify and fully characterize a novel splenic subset termed "L-DC" in relation to o...

We present two masked priming lexical decision experiments in which we examined whether a nonword prime word would activate associative/semantic information from its corresponding addition neighbor (e.g., lght-dark via the addition neighbor light), producing associative/semantic priming. The rationale was the following: If a nonword prime with a missing letter produced a semantic/associative pr...

The notion of separatedness degrees of L-fuzzy subsets is introduced in L-fuzzy topological spaces by means of L-fuzzy closure operators. Furthermore, the notion of connectedness degrees of L-fuzzy subsets is introduced. Many properties of connectedness in general topology are generalized to L-fuzzy topological spaces.

A set A of positive integers is relatively prime to n if gcd(A∪{n}) = 1. Given positive integers l ≤ m ≤ n, let Φ([l,m], n) denote the number of nonempty subsets of {l, l +1, . . . ,m} which are relatively prime to n and let Φk([l,m], n) denote the number of such subsets of cardinality k. In this paper we give formulas for these functions for the case l = 1. Intermediate consequences include id...

The following propositions are true: (1) For every sup-semilattice L and for all elements x, y of L holds ⌈⌉L(↑x∩ ↑y) = x ⊔ y. (2) For every semilattice L and for all elements x, y of L holds ⊔ L(↓x∩↓y) = x ⊓ y. (3) Let L be a non empty relational structure and x, y be elements of L. If x is maximal in (the carrier of L) \ ↑y, then ↑x \ {x} = ↑x ∩ ↑y. (4) Let L be a non empty relational structu...

We prove that (1) for any complete lattice $L$, the set $\mathcal {D}(L)$ of all non-empty saturated compact subsets Scott space $L$ is a Heyting algebra (with reverse inclusion order); and (2) if latti