Echeloned spaces

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F25%3A00635721" target="_blank" >RIV/67985840:_____/25:00635721 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1017/fms.2025.47" target="_blank" >https://doi.org/10.1017/fms.2025.47</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1017/fms.2025.47" target="_blank" >10.1017/fms.2025.47</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Echeloned spaces

Popis výsledku v původním jazyce

We introduce the notion of echeloned spaces – an order-theoretic abstraction of metric spaces. The first step is to characterize metrizable echeloned spaces. It turns out that morphisms between metrizable echeloned spaces are uniformly continuous or have a uniformly discrete image. In particular, every automorphism of a metrizable echeloned space is uniformly continuous, and for every metric space with midpoints, the automorphisms of the induced echeloned space are precisely the dilations. Next, we focus on finite echeloned spaces. They form a Fraïssé class, and we describe its Fraïssé-limit both as the echeloned space induced by a certain homogeneous metric space and as the result of a random construction. Building on this, we show that the class of finite ordered echeloned spaces is Ramsey. The proof of this result combines a combinatorial argument by Nešetřil and Hubička with a topological-dynamical point of view due to Kechris, Pestov and Todorčević. Finally, using the method of Katětov functors due to Kubiś and Mašulović, we prove that the full symmetric group on a countable set topologically embeds into the automorphism group of the countable universal homogeneous echeloned space.

Název v anglickém jazyce

Echeloned spaces

Popis výsledku anglicky

We introduce the notion of echeloned spaces – an order-theoretic abstraction of metric spaces. The first step is to characterize metrizable echeloned spaces. It turns out that morphisms between metrizable echeloned spaces are uniformly continuous or have a uniformly discrete image. In particular, every automorphism of a metrizable echeloned space is uniformly continuous, and for every metric space with midpoints, the automorphisms of the induced echeloned space are precisely the dilations. Next, we focus on finite echeloned spaces. They form a Fraïssé class, and we describe its Fraïssé-limit both as the echeloned space induced by a certain homogeneous metric space and as the result of a random construction. Building on this, we show that the class of finite ordered echeloned spaces is Ramsey. The proof of this result combines a combinatorial argument by Nešetřil and Hubička with a topological-dynamical point of view due to Kechris, Pestov and Todorčević. Finally, using the method of Katětov functors due to Kubiś and Mašulović, we prove that the full symmetric group on a countable set topologically embeds into the automorphism group of the countable universal homogeneous echeloned space.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GX20-31529X" target="_blank" >GX20-31529X: Abstraktní konvergenční schémata a jejich složitost</a><br>

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

Forum of Mathematics, Sigma

ISSN

2050-5094

e-ISSN

2050-5094

Svazek periodika

13

Číslo periodika v rámci svazku

May

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

32

Strana od-do

e89

Kód UT WoS článku

001492496000001

EID výsledku v databázi Scopus

2-s2.0-105006569089