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



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> > ***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.
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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.: 



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> > ***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.
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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. 



Stone topological Boolean algebras
I believe the paper you want is


Dona Papert Strauss, [*Topological lattices*](https://doi.org/10.1112/plms/s3-18.2.217), **Proceedings of the London Mathematical Society** (3) 18 #2 (April 1968), 217-230.


Strauss' 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, for the result I think you are asking about, in the following paper, and a copy of the following paper [is freely available at John Harding's web page](https://www.math.nmsu.edu/~jharding/2015%20Compact%20Hausdorff%20topological%20BAs.pdf).


Guram Bezhanishvili and John Harding, [*On the proof that compact Hausdorff Boolean algebras are powersets*](https://link.springer.com/article/10.1007/s11083-015-9363-y), **Order** 33 #2 (July 2016), 263-268.


