In this paper, the concepts of $L$-concave structures, concave $L$-interior operators and concave $L$-neighborhood systems are introduced. It is shown that the category of $L$-concave spaces and the category of concave $L$-interior spaces are isomorphic, and they are both isomorphic to the category of concave $L$-neighborhood systems whenever $L$ is a completely distributive lattice. Also, it i...

Derivative lattices associated with partially ordered linear spaces over skew fields are considered. Properties of the convex projective geometry $$ \mathcal{L} for a space FV field F investigated. The convexity subspaces means Abelian (ab-convexity), which is based on definition subgroup group. It shown that ab-convex directed plays theory same role as subgroups groups. We obtain element-wise ...

Many studies have investigated the lattice structure of fuzzy substructures of algebraic sets such as group and ring. Some important results about modularity and distributivity have been obtained in these studies. In this paper, we first define the notion of (normal) (λ,μ)-L-subgroups on a group and investigate some of their properties. In particular, we discuss the relationships among ordinary...

Let M = 〈M, +, <, 0, S〉 be a linear o-minimal expansion of an ordered group, and G = 〈G,⊕, eG〉 an n-dimensional group definable in M. We show that if G is definably connected with respect to the t-topology, then it is definably isomorphic to a definable quotient group U/L, for some convex ∨ definable subgroup U of 〈Mn, +〉 and a lattice L of rank equal to the dimension of the ‘compact part’ of G.

In this paper, we define the notions of fuzzy congruence relations and fuzzy convex subalgebras on a commutative residuated lattice and we obtain some related results. In particular, we will show that there exists a one to one correspondence between the set of all fuzzy congruence relations and the set of all fuzzy convex subalgebras on a commutative residuated lattice. Then we study fuzzy...

Notation and Terminology. Given a finite lattice L, the expression L ∼= [H,G] means “there exist finite groups H < G such that L is isomorphic to the interval {K | H 6 K 6 G} in the subgroup lattice of G.” A group G is called almost simple if G has a normal subgroup S P G which is nonabelian, simple, and has trivial centralizer, CG(S) = (e). If H 6 G, then the core of H in G, denoted coreG(H), ...

The lattice Lu of upper semicontinuous convex normal functions with convolution ordering arises in studies of type-2 fuzzy sets. In 2002, Kawaguchi and Miyakoshi [Extended t-norms as logical connectives of fuzzy truth values, Multiple-Valued Logic 8(1) (2002) 53–69] showed that this lattice is a complete Heyting algebra. Later, Harding et al. [Lattices of convex, normal functions, Fuzzy Sets an...

In this paper, we define the almost uniform convergence and the almost everywhere convergence for cone-valued functions with respect to an operator valued measure. We prove the Egoroff theorem for Pvalued functions and operator valued measure &theta; : R &rarr; L(P, Q), where R is a &sigma;-ring of subsets of X&ne; &empty;, (P, V) is a quasi-full locally convex cone and (Q, W) is a locally ...

The answer is yes, if ... This note attempts to give amplification to the above statement, while at the same time arriving at a reasonable description of this lattice. The main theorem of the paper is no doubt the assertion that the lattice of torsion classes of lattice-ordered groups is completely distributive. The proof of this theorem depends on the notion of a value selector, and should not...

in a previous paper, the second author established that, given finite fields $f < e$ and certain subgroups $c leq e^times$, there is a galois connection between the intermediate field lattice ${l mid f leq l leq e}$ and $c$'s subgroup lattice. based on the galois connection, the paper then calculated the irreducible, complex character degrees of the semi-direct product $c rtimes {rm gal} (e/f)$...