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reflexive bilattice; hyperreflexive bilattice; subspace lattice; bilattice
The notion of a bilattice was introduced by Shulman. A bilattice is a subspace analogue for a lattice. In this work the definition of hyperreflexivity for bilattices is given and studied. We give some general results concerning this notion. To a given lattice $\mathcal {L}$ we can construct the bilattice $\Sigma _{\mathcal {L}}$. Similarly, having a bilattice $\Sigma $ we may consider the lattice $\mathcal {L}_{\Sigma }$. In this paper we study the relationship between hyperreflexivity of subspace lattices and of their associated bilattices. Some examples of hyperreflexive or not hyperreflexive bilattices are given.
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