[Settfa] Tuesday 14/03, Jerzy Kakol

[kubis at math.cas.cz]

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 Tuesday 14th March, 10:00am 
 
  Place: IM in konírna 

 
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 Speaker:Jerzy Kakol, Adam Mickiewicz University, Poznan, Poland
 Title: On Asplund spaces C_k(X)

 Abstract  

 We continue a study about two classes of Delta-spaces and Delta_1-spaces which provide extensions of the family of Delta-sets and lambda-sets, respectively, beyond the separable metrizable spaces. A question about a characterisation of a Tychonoff space X as being a Delta_1-space by a suitable analytic property of C_k(X) or its strong dual is studied. We show that if X is omega-bounded (or Cech-complete pseudocompact), then X is scattered iff X is a Delta_1-space. Consequently, a compact space X is a Delta_1-space iff X is scattered. On the other hand, we show that if X is omega-bounded (or Cech-complete pseudocompact), then X is scattered iff C_k(X) is Asplund, i.e. every separable Banach subspace of C_k(X) has separable dual. This extends the Amir-Lindestrauss theorem.

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