University of Birmingham > Talks@bham > Analysis Seminar > Zero sets of real analytic functions and the fine topology

Zero sets of real analytic functions and the fine topology

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If you have a question about this talk, please contact Alessio Martini.

In this talk we will discuss some results concerning the zero sets of real analytic functions on open sets in Rn. We will consider the related notion of analytic uniqueness sequences and, as an application, we will show that the zero set of every non-constant real analytic function on a domain has always empty interior with respect to the fine topology (which strictly contains the Euclidean one). Further, we will see that for a certain category of sets E (containing the finely open sets), a function is real analytic on some open neighbourhood of E if and only if it is real analytic “at each point” of E. (Joint work with André Boivin and Paul Gauthier.)

This talk is part of the Analysis Seminar series.

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