Document Type
Article
Publication Date
11-1-2023
Abstract
The property of subfitness used in point-free topology (roughly speaking) to replace the slightly stronger T1-separation, appeared (as disjunctivity) already in the pioneering Wallman’s [16], then practically disappeared to reappear again (conjunctivity, subfitness), until it was in the recent decades recognized as an utmost important condition playing a very special role. Recently, it was also observed that this property (or its dual) appeared independently in general poset setting (e.g. as separativity in connection with forcing). In a recent paper [2], Delzell, Ighedo and Madden discussed it in the context of semilattices. In this article we discuss it on the background of the systems of meet-sets (subsets closed under existing infima) in posets of various generality (semilattices, lattices, distributive lattices, complete lattices) and present parallels of some localic (frame) facts, including a generalized variant of fitness.
Recommended Citation
M. Andrew Moshier, Jorge Picado & Aleš Pultr (2023) Some properties of conjunctivity (subfitness) in generalized settings, Quaestiones Mathematicae, 46:sup1, 239-252, https://doi.org/10.2989/16073606.2023.2247793
Peer Reviewed
1
Copyright
Taylor & Francis
Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial 4.0 License
Comments
This is an Accepted Manuscript version of an article accepted for publication in Quaestiones Mathematicae, volume 46, supplement 1, in 2023. https://doi.org/10.2989/16073606.2023.2247793]. It is deposited under the terms of the Creative Commons Attribution-NonCommercial License (http://creativecommons.org/licenses/by-nc/4.0/), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is properly cited.