I feel very honoured to have the possibility to contribute a paper to this volume dedicated to the memory of an outstanding mathematician and a pleasant good-humoured person: Heiner Zieschang. In 2002–2003 in M V Lomonosov Moscow State University Heiner gave a series of lectures on fixed points and coincidence theory, which I was lucky to attend. In the same period I learned the German language at his seminars. During a nice voyage in summer 2003 from Moscow to Saint Petersburg, in which I was invited to take part, I made the acquaintance with his wife Ute and daughter Kim; two years later I met his other daughter Tanja. Heiner guided my study of coincidences, intersections and preimages during my visit in November–December 2004 in Ruhr-Universität Bochum. It was planned, to continue the project in 2005. But that hope was doomed to disappointment….