Abbreviation: DblStAlg
A \emph{double Stone algebra} is a structure $\mathbf{L}=\langle L,\vee ,0,\wedge ,1,^*\rangle $ such that
$\langle L,\vee,0,\wedge,1,^*\rangle $ is a Stone algebras
$\langle L,\wedge,1,\vee,0,^*\rangle $ is a Stone algebras
Let $\mathbf{L}$ and $\mathbf{M}$ be double Stone algebras. A morphism from $\mathbf{L}$ to $\mathbf{M}$ is a function $h:L\rightarrow M$ that is a homomorphism:
$h(x\vee y)=h(x)\vee h(y)$, $h(x\wedge y)=h(x)\wedge h(y)$, $h(0)=0 $, $h(1)=1$, $h(x^*)=h(x)^*$
Example 1:
$\begin{array}{lr}
f(1)= &1
f(2)= &1
f(3)= &1
f(4)= &
f(5)= &
f(6)= &
f(7)= &
\end{array}$