I am looking for an initial reference for a theorem which is known, namely:

: A Boolean algebra $A$ admits a Stone space topology (i.e. is the underlying algebra of a Stone topological algebra)Theoremiff$A$ is isomorphic to $\mathcal{P}(S)$, where $S$ is a set and a power-set $\mathcal{P}(S)$ is equiped with product topology.

The proposition can be found e.g. in book *Stone spaces* (**Corollary** in VI.3.2 *Stone-type dualities* pp. 247 of 2002 edition) by P. Johnstone. I am going to cite it in a paper but it is given there without any reference on the original, initial proof, in a fashion of a folklore result.

I heаrd somewhere that it is Strauss theorem (but don't know which Strauss is it, is it Dona Strauss, may be not). Anyway I need to cite an author and paper.

Thanks for kindness and effort in advance.

**Edit:** Dave L Renfro pointed me to the paper of Dona Strauss where the following result is proven by means of Pontryagin duality.:

If a Boolean algebra $A$ admits a compact Hausdorff topology (i.e. is the underlying algebra of a compact Hausdorff topological algebra) then $A$ is isomorphic to $\mathcal{P}(S)$ where $S$ is a set and a power-set $\mathcal{P}(S)$ is equipped with product topology.Theorem:

as well he pointed me to the paper of Guram Bezhanishvili and John Harding, where them provide simplified proof without use of Pontryagin duality. On that I remembered that I once even discussed the paper with John. Since the last result is enough for me, I accept the answer. Thank you Dave L Renfro.

Topological lattices,Proceedings of the London Mathematical Society(3) 18 #2 (April 1968), 217-230. The paper is behind a paywall and I do not have access to it (without travelling to a nearby university library). However, Strauss' paper is cited inOn the proof that compact Hausdorff Boolean algebras are powersetsby Guram Bezhanishvili and John Harding, which is freely available. $\endgroup$6more comments