Based on a complete Heyting algebra, we modify the definition of lattice-valued fuzzifying convergence space using fuzzy inclusion order and construct in this way a Cartesian-closed category, called the category of L−ordered fuzzifying convergence spaces, in which the category of L−fuzzifying topological spaces can be embedded. In addition, two new categories are introduced, which are called th...

In this paper, we discuss the equivalent conditions of pretopological and topological $L$-fuzzy Q-convergence structures and define $T_{0},~T_{1},~T_{2}$-separation axioms in $L$-fuzzy Q-convergence space. {Furthermore, $L$-ordered Q-convergence structure is introduced and its relation with $L$-fuzzy Q-convergence structure is studied in a categorical sense}.

For any BL-algebra L, we construct an associated lattice ordered Abelian group GL that coincides with the Chang’s `-group of an MV-algebra when the BL-algebra is an MValgebra. We prove that the Chang’s group of the MV-center of any BL-algebra L is a direct summand in GL. We also find a direct description of the complement S(L) of the Chang’s group of the MV-center in terms of the filter of dens...

A partially ordered set (X, is called sharply transitive if its automorphism group is sharply transitive on X, that is, it is transitive and the stabilizer of every element is triviaL It is shown that every free group is the automorphism group of a sharply transitive partially ordered set. It is also shown that there exists a sharply transitive partially ordered set (-,Y, :::;) having some maxi...

We study the multiplicative lattices L which satisfy condition a = (a : b))(a b) for all a, b ∈ L. Call them sharp lattices. prove that every totally ordered lattice is isomorphic to ideal of valuation domain with value group ℤ or ℝ. A localized at its maximal elements are The converse true if has finite character.