学术动态

#RAFS^†Session 15

Time：Apr. 23, 2021, 10:00--12:00

Location：434 Qi Xiang Building, Chang'an Campus

Title：Absolute G-delta

Abstract：We realize the importance of G-delta sets on severaloccasions—e.g., the set of points of continuity of a real-valued function is a G-delta, and a setEin Baire space is residual if and only ifEcontains a dense G-delta subset. In this talk, complete metrizability, or topological completeness, proves to serve as a third source. We will show that any non-empty G-delta subset of a complete metric space is topologically complete and, conversely, if a setXof a metric spaceZis topologically complete, thenXis a G-delta subset ofZ, thus identifying the key property of an absolute G-delta, which in turn is a basic notion in descriptive set theory.

† Real Analysis Friday Seminars. Contactshuangshen@nwpu.edu.cnfor any inquiry. For a history of this seminar, please visithttps://teacher.nwpu.edu.cn/2017010194.