科研之友
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摘要
It is known that if E is a closed subset of an open Riemann surface R and f is a holomorphic function on a neighbourhood of E, then it is "usually" not possible to approximate f uniformly by functions holomorphic on all of R. We show, however, that for every open Riemann surface R and every closed subset E subset of R, there is closed subset F subset of E that approximates E extremely well, such that every function holomorphic on F can be approximated much better than uniformly by functions holomorphic on R.
- 出版日期2017-6
