Year: 2026
Type: preprint
Abstract: The Wagner-Preston theorem states that every inverse semigroup can be embedded into an inverse semigroup of partial bijections on some set. However, this embedding does not respect lattice operations in the natural ordering. In this paper, we show that an abstract pseudogroup can be faithfully represented by partial bijections on a set if and only if its frame of idempotents is spatial. More generally, we show that any abstract pseudogroup can be faithfully represented by partial homeomorphisms on a locale.
Source: arXiv (Cornell University)
Author: Wrigley, Joshua L.
Institution: Masaryk University
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214926026