Using whales to complete a Boolean algebra (Q1407454)

Let \(B\) be a Boolean algebra and \(A\) be a subset of \(B\). Then \(A\) is called a whale of \(B\) if (1) \(a\in A,\) \(b\in B\) and \(b \leq a\) imply \(b\in A\); (2) sup\(\{a \mid a\in A\}=1\). The author uses the whales of \(B\) to construct the completion of \(B\). This construction leads immediately to the assertion that any Boolean algebra can be represented as a dense subalgebra of all bands of an Archimedean Riesz space.