On strongly-convex subtrellises of a trellis

Abstract

The set $CS(L)$ of all convex sublattices of a lattice $L$, excluding $\emptyset$, was studied by S. Lavanya and S. P. Bhatta using the partial order $\leq$, defined as follows: for $A, B \in CS(L)$, $A \leq B$ if and only if 'for each $a \in A$, there is  $b\in B$ such that $a \leq b$' and 'for each $b \in B$, there is  $a \in A$ such that $a \leq b$'. They showed that $(CS(L), \leq)$ is a lattice such that both $L$ and $CS(L)$ lie in the same equational class. Also, they obtained many significant results concerning $CS(L)$. The present paper generalizes many of these results along with some related results of others, from lattices to trellises, by introducing the notion of 'strongly-convex subtrellises' in trellises in place of 'convex sublattices' in lattices.