Dualities for subresiduated lattices

A subresiduated lattice is a pair (A, D), where bounded distributive lattice, D sublattice of and for every $$a,b\in A$$ there $$c\in D$$ such that all $$d\in , $$d\wedge a\le b$$ if only $$d\le c$$ . This c denoted by $$a\rightarrow can be regarded as an algebra $$\left$$ type (2, 2, 0, 0) $$D=\{a\in A\mid 1\rightarrow a=a\}$$ The class lattices variety which properly contains to the Heyting algebras. In this paper we present dual equivalences algebraic category lattices. More precisely, develop spectral style duality bitopological category. Finally study connections these results with known Priestley