Stone Duality for Kolmogorov locally small spaces
Authors:
- Artur Piękosz
Abstract
In this paper, we prove new versions of Stone Duality. The main version is the following: the category of Kolmogorov locally small spaces and bounded continuous mappings is equivalent to the category of spectral spaces with decent lumps and with bornologies in the lattices of (quasi-) compact open sets as objects and spectral mappings respecting those decent lumps and satisfying a boundedness condition as morphisms. Furthermore, it is dually equivalent to the category of bounded distributive lattices with bornologies and with decent lumps of prime filters as objects and homomorphisms of bounded lattices respecting those decent lumps and satisfying a domination condition as morphisms. This helps to understand Kolmogorov locally small spaces and morphisms between them. We comment also on spectralifications of topological spaces.
- Record ID
- CUT659b5948e1fb43ef9056ae58021a3240
- Publication categories
- ;
- Author
- Journal series
- Symmetry, ISSN , e-ISSN 2073-8994, Monthly
- Issue year
- 2021
- Vol
- 13
- No
- 10
- Pages
- [1-17]
- Article number
- 1791
- Other elements of collation
- Bibliografia (na s.) - 17; Bibliografia (liczba pozycji) - 32; Oznaczenie streszczenia - Abstr.; Numeracja w czasopiśmie - Vol. 13, Iss. 10, Spec. Iss.
- Substantive notes
- Special Issue: Recent Advance in Pure and Applied Mathematics
- Keywords in English
- Stone Duality, spectral space, distributive lattice, locally small space, equivalence of categories, spectralification
- DOI
- DOI:10.3390/sym13101791 Opening in a new tab
- URL
- https://www.mdpi.com/2073-8994/13/10/1791 Opening in a new tab
- Language
- eng (en) English
- License
- Score (nominal)
- 70
- Additional fields
- Indeksowana w: Web of Science, Scopus
- Uniform Resource Identifier
- https://cris.pk.edu.pl/info/article/CUT659b5948e1fb43ef9056ae58021a3240/
- URN
urn:pkr-prod:CUT659b5948e1fb43ef9056ae58021a3240
* 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.