Representing lattices by homotopy groups of graphs
In this paper we represent every lattice by subgroups of free groups using the concept of the homotopy group of a graph.
In this paper we represent every lattice by subgroups of free groups using the concept of the homotopy group of a graph.
In [2], J. Klimes studied rotations of lattices. The aim of the paper is to research rotations of the so-called -lattices introduced in [3] by V. Snasel.
For lattices of finite length there are many characterizations of semimodularity (see, for instance, Grätzer [3] and Stern [6]–[8]). The present paper deals with some conditions characterizing semimodularity in lower continuous strongly dually atomic lattices. We give here a generalization of results of paper [7].
We investigate the congruence lattices of lattices in the varieties . Our approach is to represent congruences by open sets of suitable topological spaces. We introduce some special separation properties and show that for different n the lattices in have different congruence lattices.
In this paper we investigate the system Conv of all sequential convergences on a distributive lattice .
The notion of sequential convergence on a lattice is defined in a natural way. In the present paper we investigate the system of all sequential convergences on a lattice .