The author studies \(\sigma\)-complete Boolean algebras and their intrinsic topologies. Theorem 1. Let B be a \(\sigma\)-complete Boolean algebra which contains an infinite \(\sigma\)-independent subset. Let \({\mathcal T}\) be a topology on B such that (1) if a sequence \((x_ n)\) in B either increases or decreases to some \(x\in B\), then \((x_ n)\) converges to x in \({\mathcal T}\), (2) the function \(x\mapsto 1-x\) is continuous in \({\mathcal T}\), and (3) each \(\sigma\)-subring of B is closed in \({\mathcal T}\). Then the space (B,\({\mathcal T})\) is not regular and, therefore, the Boolean operations \(x+y\), \(x\vee y\), xy and x-y are discontinuous in \({\mathcal T}.\) If \({\mathcal T}\) is taken to be the sequential (o)-topology on \(2^ X\) for some uncountable set X, then Theorem 1 gives an answer to a 1975 question of L. Ya. Savel'ev. The author proves also some properties of non-atomic Borel measures on uncountable Polish spaces.