On orders of two transformation semigroups of the boolean - Livinsky, I.V.; Zhukovska, T.G. (Carpathian Mathematical Publications, 2014)
We consider the semigroup $\mathcal{O}(\mathcal{B}_n)$ of all order-preserving transformations $φ : \mathcal{B}_n → \mathcal{B}_n$ of ordered by inclusion boolean $\mathcal{B}_n$ of $n$-element set (i.e. such transformations that $A \subseteq B$ implies $φ(A) \subseteq φ(B)$) and its subsemigroup $\mathcal{C}(\mathcal{B}_n)$ of those transformations for which $φ(A) \subseteq A$ for all $A \in \mathcal{B}_n$. Orders of these semigroups are calculated.