On the Conjecture of Wood and Projective Homogeneity

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17610%2F18%3AA1901I37" target="_blank" >RIV/61988987:17610/18:A1901I37 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1016/j.jmaa.2017.12.051" target="_blank" >http://dx.doi.org/10.1016/j.jmaa.2017.12.051</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.jmaa.2017.12.051" target="_blank" >10.1016/j.jmaa.2017.12.051</a>

Jazyk výsledku

angličtina

Název v původním jazyce

On the Conjecture of Wood and Projective Homogeneity

Popis výsledku v původním jazyce

In 2005 Kawamura and Rambla, independently, constructed ametric counterexample to Wood's Conjecture from 1982. We exhibit a newnonmetric counterexample of a spaceL?, such that C_0(L?,C) is almost transitive,and show that it is distinct from a nonmetric space whose existencefollows from the work of Greim and Rajagopalan in 1997. Up to ourknowledge, this is only the third known counterexample to Wood'sConjecture. We also show that, contrary to what was expected, if a onepointcompactification of a space X is R.H. Bing's pseudo-circle thenC_0(X,C) is not almost transitive, for a generic choice of points.Finally, we point out close relation of these results on Wood'sconjecture to a work of Irwin and Solecki on projective Fra¨?ss´e limitsand projective homogeneity of the pseudo-arc and, addressingtheir conjecture, we show that the pseudo-circle is not approximatelyprojectively homogeneous.

Název v anglickém jazyce

On the Conjecture of Wood and Projective Homogeneity

Popis výsledku anglicky

In 2005 Kawamura and Rambla, independently, constructed ametric counterexample to Wood's Conjecture from 1982. We exhibit a newnonmetric counterexample of a spaceL?, such that C_0(L?,C) is almost transitive,and show that it is distinct from a nonmetric space whose existencefollows from the work of Greim and Rajagopalan in 1997. Up to ourknowledge, this is only the third known counterexample to Wood'sConjecture. We also show that, contrary to what was expected, if a onepointcompactification of a space X is R.H. Bing's pseudo-circle thenC_0(X,C) is not almost transitive, for a generic choice of points.Finally, we point out close relation of these results on Wood'sconjecture to a work of Irwin and Solecki on projective Fra¨?ss´e limitsand projective homogeneity of the pseudo-arc and, addressingtheir conjecture, we show that the pseudo-circle is not approximatelyprojectively homogeneous.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/LQ1602" target="_blank" >LQ1602: IT4Innovations excellence in science</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2018

Kód důvěrnosti údajů

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

Název periodika

J MATH ANAL APPL

ISSN

0022-247X

e-ISSN

—

Svazek periodika

—

Číslo periodika v rámci svazku

461

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

15

Strana od-do

1733-1747

Kód UT WoS článku

000426334400038

EID výsledku v databázi Scopus

2-s2.0-85039164503