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PreprintCC BY 4.0arXiv

Representation of abstract pseudogroups

  • Joshua L. Wrigley
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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.

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Cite

BibTeXRIS
BibTeX
@misc{wrigley2026representation,
  title = {{Representation of abstract pseudogroups}},
  author = {Joshua L. Wrigley},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.37124},
  eprint = {2609.37124},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.37124},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Representation of abstract pseudogroups
AU  - Joshua L. Wrigley
PY  - 2026
DA  - 2026/09/29
PB  - arXiv
DO  - 10.48550/arxiv.2609.37124
UR  - https://arxiv.org/abs/2609.37124
AB  - 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.
ER  -