8
$\begingroup$

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.

$\endgroup$
3
$\begingroup$

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.

| cite | improve this answer | |
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.