David Uhrik: Composing discontinuous functions

Dear all,

The seminar meets on Wednesday October 31st at 11:00 in the Institute of
Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.

Program: David Uhrik — Composing discontinuous functions

In this talk we’ll look at composing functions from the Young hierarchy,
which is defined similarly as the well-known Baire hierarchy of
functions but we only consider monotone sequences. It will be shown that
these compositions behave nicely, i.e. the resulting function is again
an element of the hierarchy and its rank is bounded above. On the other
hand we can decompose these functions into a composition of two with
lower rank. In the end I’ll say something about the “failed” attempt to
generalise this hierarchy to convergence according to an ideal.


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