Abstract:
The questions of the standardness of quasivarieties have been investigated by many authors. The problem
"Which finite lattices generate a standard topological prevariety?" was suggested by D.M. Clark, B.A. Davey,
M.G. Jackson and J.G. Pitkethly in 2008. We continue to study the standardness problem for one specific
finite modular lattice which does not satisfy all Tumanov’s conditions. We investigate the topological
quasivariety generated by this lattice and we prove that the researched quasivariety is not standard, as
well as is not finitely axiomatizable. We also show that there is an infinite number of lattices similar to the
lattice mentioned above.
