Are finite affine topological systems worthy of study?

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Are finite affine topological systems worthy of study?

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Are finite affine topological systems worthy of study?

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2023

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

FUZZY SETS AND SYSTEMS

ISSN

0165-0114

e-ISSN

0165-0114

Svazek periodika

466

Číslo periodika v rámci svazku

AUG 30 2023

Stát vydavatele periodika

CZ - Česká republika

Počet stran výsledku

11

Strana od-do

1-11

Kód UT WoS článku

001013270900001

EID výsledku v databázi Scopus

2-s2.0-85146936298