License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CSL.2021.32
URN: urn:nbn:de:0030-drops-134660
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2021/13466/
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Lopez, Aliaume

Preservation Theorems Through the Lens of Topology

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LIPIcs-CSL-2021-32.pdf (0.6 MB)

Abstract

In this paper, we introduce a family of topological spaces that captures the existence of preservation theorems. The structure of those spaces allows us to study the relativisation of preservation theorems under suitable definitions of surjective morphisms, subclasses, sums, products, topological closures, and projective limits. Throughout the paper, we also integrate already known results into this new framework and show how it captures the essence of their proofs.

BibTeX - Entry

@InProceedings{lopez:LIPIcs:2021:13466,
  author =	{Aliaume Lopez},
  title =	{{Preservation Theorems Through the Lens of Topology}},
  booktitle =	{29th EACSL Annual Conference on Computer Science Logic (CSL 2021)},
  pages =	{32:1--32:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-175-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{183},
  editor =	{Christel Baier and Jean Goubault-Larrecq},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/13466},
  URN =		{urn:nbn:de:0030-drops-134660},
  doi =		{10.4230/LIPIcs.CSL.2021.32},
  annote =	{Keywords: Preservation theorem, Pre-spectral space, Noetherian space, Spectral space}
}

Keywords: Preservation theorem, Pre-spectral space, Noetherian space, Spectral space
Collection: 29th EACSL Annual Conference on Computer Science Logic (CSL 2021)
Issue Date: 2021
Date of publication: 13.01.2021

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