PERFECTLY EVERYWHERE SURJECTIVE BUT NOT JONES FUNCTIONS

Speaker(s)

TOMASZ NATKANIEC

Affiliation

University of Gdańsk

Date

Feb. 28, 2018, 4:15 p.m.

Room

room 5050

Seminar

Topology and Set Theory Seminar

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Given a function f : R → R we say that • f is perfectly surjective (f ∈ PES) if f[P] = R for every perfect set P; • f is a Jones function (f ∈ J) if C ∩ f is non-empty for every closed C ⊂ R^2 with dom(C) of size c. M. Fenoy-Munoz, J.L. Gamez-Merino, G.A. Munoz-Fernandez and E. Saez-Maestro in the paper "A hierarchy in the family of real surjective functions" [Open Math. 15 (2017), 486–501] asked about the lineability of the set PES \ J. Answering this question we show that the class PES \ J is c^+ -lineable. Moreover, if 2^