A zero-dimensional (Hausdorff) space is a space such that the set of all "open-and-closed" sets is a basis for the topology. A non-archimedean space is a space with a basis for the topology such that any two basic sets either are disjoint or one contains the other.

In the P. Nyikos' paper "A Survey of zero-dimensional spaces" (Topology (Proc. 9th Annual Spring Conf. Memphis, 1975), M. Dekker (1976) pp. 87–114) is stated that every compact zero-dimensional space is non-archimedean, but he doesn't prove it (moreover, he doesn't cite any explicit reference for this fact).

Do you know a reference for this fact? I'm interested in the proof.


There is a reference to this result in this paper by Nyikos on page 6 (top). The reference does not contain the proof of it, while section $2$ of the linked paper does give a proof.

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