On the connectivity of graph Lipscomb's spaces

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F25%3A00603075" target="_blank" >RIV/67985840:_____/25:00603075 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1007/s11784-024-01150-7" target="_blank" >https://doi.org/10.1007/s11784-024-01150-7</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s11784-024-01150-7" target="_blank" >10.1007/s11784-024-01150-7</a>

Jazyk výsledku

angličtina

Název v původním jazyce

On the connectivity of graph Lipscomb's spaces

Popis výsledku v původním jazyce

A central role in topological dimension theory is played by Lipscomb’s space JA since it is a universal space for metric spaces of weight |A|≥ℵ0. On the one hand, Lipscomb’s space is the attractor of a possibly infinite iterated function system, i.e. it is a generalized Hutchinson-Barnsley fractal. As, on the other hand, some classical fractal sets are universal spaces, one can conclude that there exists a strong connection between topological dimension theory and fractal set theory. A generalization of Lipscomb’s space, using graphs, has been recently introduced (see Miculescu and Mihail in Aequat Math, 96:1141–1157, 2022). It is denoted by JAG and is called the graph Lipscomb’s space associated with the graph G on the set A. It turns out that it is a topological copy of a generalized Hutchinson-Barnsley fractal. This paper provides a characterization of those graphs G for which JAG is connected. In the particular case when A is finite, some supplementary characterizations are presented.

Název v anglickém jazyce

On the connectivity of graph Lipscomb's spaces

Popis výsledku anglicky

A central role in topological dimension theory is played by Lipscomb’s space JA since it is a universal space for metric spaces of weight |A|≥ℵ0. On the one hand, Lipscomb’s space is the attractor of a possibly infinite iterated function system, i.e. it is a generalized Hutchinson-Barnsley fractal. As, on the other hand, some classical fractal sets are universal spaces, one can conclude that there exists a strong connection between topological dimension theory and fractal set theory. A generalization of Lipscomb’s space, using graphs, has been recently introduced (see Miculescu and Mihail in Aequat Math, 96:1141–1157, 2022). It is denoted by JAG and is called the graph Lipscomb’s space associated with the graph G on the set A. It turns out that it is a topological copy of a generalized Hutchinson-Barnsley fractal. This paper provides a characterization of those graphs G for which JAG is connected. In the particular case when A is finite, some supplementary characterizations are presented.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2025

Kód důvěrnosti údajů

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

Název periodika

Journal of Fixed Point Theory and Applications

ISSN

1661-7738

e-ISSN

1661-7746

Svazek periodika

27

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

17

Strana od-do

1

Kód UT WoS článku

001374775800001

EID výsledku v databázi Scopus

2-s2.0-85212140141