This note (download) contains an example of nowhere continuous (weakly) Picard operator and a motivation to consider such a function. It was presented during the following talks:

• O pewnym uogólnieniu równania Steinhausa (in Polish) [About some generalization of Steinhaus functional equation] (meeting no. 1291 of the chair of functional equations, Katowice, 08.01.2013),
• Some remarks on weakly Picard operators and their application in functional equations (9th international Students' Conference on analysis, Ustroń, 03.02.2013).