Academy of Mathematics and Systems Science, CAS Colloquia & Seminars
Mr. Ming Xiao，University of Toronto
A Borel Chain Condition of T(X)
Time & Venue:
2019.8.13 14:00-16:00 N902
In 1948, Horn and Tarski conjectured whether the $\sigma$-finite chain condition and $\sigma$-bounded chain condition are equivalent. The first counter example was given by Thummel in 2012 and then a Borel counter example was given by Todorvevic in 2014. Both examples belong to a class of poset called "Todorvevic ordering" $T(X)$ over topological spaces $X$. In this talk, I will illustrate a satisfactory condition for a topological space $X$ making the corresponding poset $T(X)$ fail to have a countable Borel partition witenessing the $\sigma$ finite chain condition , although it may still witnessed by non Borel partitions.
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