On the Conjecture of Wood and Projective Homogeneity

Result code in 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>
Result on the web
<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>

Result language
angličtina
Original language name
On the Conjecture of Wood and Projective Homogeneity
Original language description
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.
Czech name
—
Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/LQ1602" target="_blank" >LQ1602: IT4Innovations excellence in science</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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