I am looking for an initial reference for a theorem which is known, namely:
Theorem: A Boolean algebra $A$ admits a Stone space topology (i.e. is the underlying algebra of a Stone topological algebra) iff $A$ 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.:
Theorem: 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.
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.
