On non-archimedean frames

Francisco Ávila; Miriam Bocardo-Gaspar; Julio Urenda; Angel Zaldívar

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arXiv · 2311.18095

On non-archimedean frames

Francisco Ávila·Miriam Bocardo-Gaspar·Julio Urenda·Angel Zaldívar

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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.

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BibTeX RIS

Francisco Ávila, Miriam Bocardo-Gaspar, Julio Urenda, Angel Zaldívar. 2025-09-13. On non-archimedean frames. https://arxiv.org/abs/2311.18095

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