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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.


This is an Accepted Manuscript version of an article accepted for publication in Quaestiones Mathematicae, volume 46, supplement 1, in 2023.]. It is deposited under the terms of the Creative Commons Attribution-NonCommercial License (, which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Available for download on Friday, November 01, 2024