[Settfa] Tuesday 28/11, Jacopo Somaglia

[kubis at math.cas.cz]

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 Tuesday 28th November, 10:00am 
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 Speaker:Jacopo Somaglia, Charles University in Prague / Università degli Studi di Milano
 Title: New examples of non-commutative Valdivia compact spaces

 Abstract  
A non-commutative Valdivia compact space is a compact space with retractional skeleton. A compact space is Valdivia if and only if it has a commutative retractional skeleton. The two classes do not agree: the ordinal space $[0,\omega_2]$, endowed with the interval topology, is an easy and well-known example of a non-commutative Valdivia compact space that is not Valdivia. In this talk, I will recall the definition and some properties of the Coarse wedge topology on trees. A characterization of non-commutative Valdivia trees will be presented. This characterization will be used to give a negative answer to the following question:


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\textit{Let $X$ be a non-commutative Valdivia compact space that does not contain any copy of the ordinal space $[0,\omega_2]$. Is $X$ necessarily Valdivia?}


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 For more information see the seminar web page at 
 https://calendar.math.cas.cz/set-theory-and-analysis-actual .