Abstract
Every finitary algebra is, of course, a topological algebra in the discrete topology. On the other hand, a topological Boolean σ-algebra is indiscrete; sequences (0, 0, …, x, x,…) with join x converge to (0, 0,…) with join 0, so 0 is in {x}−, and similarly x is in {0}−. For lattices with infinite joins but only finite meets, such as topologies, the matter is more interesting.
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