[Settfa] Tuesday 08/03, Jerzy Kakol

[kubis at math.cas.cz]

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 Tuesday 8th March, 10:00am 
 
  Place: IM in konírna 

 
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 Speaker:Jerzy Kakol, IM CAS
 Title: On $\Delta$-spaces $X$ and their characterization in terms of spaces $C_{p}(X)$

 Abstract  

 A topological space $X$ is called a $\Delta$ -space if for every decreasing sequence $(D_n)$ of subsets of $X$ with empty intersection there is a decreasing sequence $(V_n)$ of open subsets of $X$, $D_n\subset V_n$ for every $n$ with empty intersection. We proved that $X$ is a $\Delta$-space if and only if $C_p(X)$ is distinguished, i.e. the dual of $C_p(X)$ endowed with the topology of the uniform convergence on $C_p(X)$- bounded sets carries the finest locally convex topology. This analytic approach provided several new results about $\Delta$-sets and $\Delta$-spaces. Among the others we proved that every Cech-complete $\Delta$-space is scattered and every scattered Eberlein compact space is a $\Delta$-space. Nevertheless, compact scattered spaces X not being a $\Delta$-space do exist. Applications for Banach spaces $C(K)$ and spaces $C_p(K)$ are obtained.

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