Abstract:
We pose the problem of minimization for the relative preimage
problem and prove a minimization theorem.
The relative common
preimage problem for a finite system of maps, whose particular
cases are the relative coincidence and common root problems for
finitely many maps, is reduced to the relative preimage problem.
As corollaries, results concerning the relative coincidence
problems for two maps, problems of fixed points and roots are
obtained; these results, with certain distinctions, can be found
in known papers by other authors.
Keywords:smooth manifold, map of pairs, preimage points, minimization problem, Nielsen numbers, fixed point, common roots.
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