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We prove that order convergence on a Boolean algebra turns it into a compactconvergence space if and only if this Boolean algebra is complete and atomic.We also show that on an Archimedean vector lattice, order intervals are compactwith respect to order convergence if and only the vector lattice is completeand atomic. Additionally we provide a direct proof of the fact that uoconvergence on an Archimedean vector lattice is induced by a topology if andonly if the vector lattice is atomic.

Atomicity of Boolean algebras and vector lattices in terms of order convergence