#### İstanbul Analysis Seminars

Quotients of Irrationals
Nurettin Ergun
Marmara University, Turkey
Özet : As is well-known, a continuous image of a separable and completely metrizable space is called in Topology as analytic set or analytic space. The following theorems Baire-Alexandroff Theorem (1929): A topological space $X$ is homeomorphic to $\mathbb{P}$ iff X is a separable, 0-dimensional and metrizable space which is an absolute $G_\delta$ having no compact open subset. Hausdorff Theorem (1932): A metric space is an analytic set iff it is a continuous image In the above setting, $\mathbb{P}$ denotes the irrationals with the standard subspace topology obtained . We will give a detailed proof in this talk of the following well-known theorem of Ernest Michael and Arthur H. Stone from 1969: The Main Theorem: Every analytic set is actually an image of $\mathbb{P}$ under a quotient mapping.
 Tarih : 06.11.2015 Saat : 15:40 Yer : Sabancı University, Karaköy Communication Bankalar Caddesi 2, Karaköy Dil : English