Esakia Duality for Heyting small spaces
Authors:
- Artur Piękosz
Abstract
We continue our research plan of developing the theory of small and locally small spaces, proposing this theory as a realisation of Grothendieck’s idea of tame topology on the level of general topology. In this paper, we develop the theory of Heyting small spaces and prove a new version of Esakia Duality for such spaces. To do this, we notice that spectral spaces may be seen as sober small spaces with all smops compact and introduce the method of the standard spectralification. This helps to understand open continuous definable mappings between definable spaces over o-minimal structures.
- Record ID
- CUTca6430c97ff4464f81bc6950101f4eb9
- Publication categories
- ;
- Author
- Journal series
- Symmetry, ISSN , e-ISSN 2073-8994, Monthly
- Issue year
- 2022
- Vol
- 14
- No
- 12
- Pages
- [1-13]
- Article number
- 2567
- Other elements of collation
- Bibliografia (na s.) - 12-13; Bibliografia (liczba pozycji) - 39; Oznaczenie streszczenia - Abstr.; Numeracja w czasopiśmie - Vol. 14, Iss. 12
- Substantive notes
- Special Issue: The Study of Lattice Theory and Universal Algebra
- Keywords in English
- Esakia Duality, small space, spectral space, Heyting algebra, tame topology
- ASJC Classification
- ; ; ;
- DOI
- DOI:10.3390/sym14122567 Opening in a new tab
- URL
- https://www.mdpi.com/2073-8994/14/12/2567 Opening in a new tab
- Language
- eng (en) English
- License
- Score (nominal)
- 70
- Score source
- journalList
- Score
- Publication indicators
- Additional fields
- Indeksowana w: Web of Science, Scopus
- Uniform Resource Identifier
- https://cris.pk.edu.pl/info/article/CUTca6430c97ff4464f81bc6950101f4eb9/
- URN
urn:pkr-prod:CUTca6430c97ff4464f81bc6950101f4eb9
* presented citation count is obtained through Internet information analysis, and it is close to the number calculated by the Publish or PerishOpening in a new tab system.