On Compact Topological Lattices of Finite Dimension

On generalized topological molecular lattices

In this paper, we introduce the concept of the generalized topological molecular lattices as a generalization of Wang's topological molecular lattices,  topological spaces, fuzzy topological spaces, L-fuzzy topological spaces and soft topological spaces. Topological molecular lattices were defined by closed elements, but in this new structure we present the concept of the open elements and defi...

Topological Residuated ‎Lattices

In this paper, we study the separtion axioms $T_0,T_1,T_2$ and $T_{5/2}$ on topological and semitopological residuated lattices and we show that they are equivalent on topological residuated lattices. Then we prove that for every infinite cardinal number $alpha$, there exists at least one nontrivial Hausdorff topological residuated lattice of cardinality $alpha$. In the follows, we obtain some ...

Some properties of b-weakly compact operators on Banach lattices

In this paper we give some necessary and sufficient conditions for which each Banach lattice  is    space and we study some properties of b-weakly compact operators from a Banach lattice  into a Banach space . We show that every weakly compact operator from a Banach lattice  into a Banach space  is b-weakly compact and give a counterexample which shows that the inverse is not true but we prove ...

Minkowski’s Conjecture, Well-rounded Lattices and Topological Dimension

On the Homological Dimension of Lattices

Let L be a finite lattice and let L̂ = L − {0̂, 1̂}. It is shown that if the order complex ∆(L̂) satisfies H̃k−2 ( ∆(L̂) ) 6= 0 then |L| ≥ 2k. Equality |L| = 2k holds iff L is isomorphic to the Boolean lattice {0, 1}k.