Are finite affine topological systems worthy of study?
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F60460709%3A41310%2F23%3A96638" target="_blank" >RIV/60460709:41310/23:96638 - isvavai.cz</a>
Result on the web
<a href="https://www.sciencedirect.com/science/article/pii/S0165011422005127?via%3Dihub" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0165011422005127?via%3Dihub</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00500-022-07260-z" target="_blank" >10.1007/s00500-022-07260-z</a>
Alternative languages
Result language
angličtina
Original language name
Are finite affine topological systems worthy of study?
Original language description
There exists the notion of topological system of S. Vickers, which provides a common framework for both topological spaces and the underlying algebraic structures of their topologies-locales. A well-known result of S. A. Morris states that every topological space is homeomorphic to a subspace of a product of a finite (three-element) topological space. We have already shown that the space of S. A. Morris is (in general) no longer finite in case of affine topological spaces (inspired by the concept of affine set of Y. Diers), which include many-valued topology. This paper provides an analogue of the result of S. A. Morris for topological systems of S. Vickers, and also shows that for affine topological systems, an analogue of the above three-element space becomes (in general) infinite. A simple message here is that finite systems play a (probably) less important role in the affine topological setting (for example, in many-valued topology) than they do play in the classical topology.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
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Continuities
S - Specificky vyzkum na vysokych skolach
Others
Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
FUZZY SETS AND SYSTEMS
ISSN
0165-0114
e-ISSN
0165-0114
Volume of the periodical
466
Issue of the periodical within the volume
AUG 30 2023
Country of publishing house
CZ - CZECH REPUBLIC
Number of pages
11
Pages from-to
1-11
UT code for WoS article
001013270900001
EID of the result in the Scopus database
2-s2.0-85146936298