We find conditions on topological spaces X, Y and nonempty subset
B of Y which guarantee that for each continuous map
f:X→ Y there exists a map g∼ f such that
Nielsen preimage classes of g-1(B) are all topologically
essential.
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….
Keywords
preimage problem, Nielsen preimage class,
topological essentiality, Nielsen preimage number, minimum
number of preimage classes
Chair of General Topology and
Geometry
Faculty of Mechanics and Mathematics
M V Lomonosov Moscow State University
Leninskie Gori, 119991 Moscow, GSP-1
Russia