On non-archimedean frames
Abstract
In this investigation, we introduce the class of non-archimedean frames in spirit with the topological notion of non-archimedean spaces. We explore various properties of these frames - particularly their spaciality. We attach a base that constitutes a tree to each non-archimedean frame, and then we observe that every non-archimedean frame is a quotient of the frame of opens of the tree's branch space. Moreover, we give a partial answer to when these frames are canonically isomorphic; this leads to considering some choice principles of the resulting tree.
Cite
@article{arxiv.2311.18095,
title = {On non-archimedean frames},
author = {Francisco Ávila and Miriam Bocardo-Gaspar and Julio Urenda and Angel Zaldívar},
journal= {arXiv preprint arXiv:2311.18095},
year = {2025}
}
Comments
19 pages, 3 figures, several changes has been made on the introduction, preliminaries, in particular a corection to the statement: all non-archimedean frames are spatial, is incorrect, an example of this is provided with some particular statement about the spatiality of these frames