Minimizing the number of Nielsen preimage classes

TL;DR

This paper establishes conditions on topological spaces that ensure the existence of homotopic maps with all Nielsen preimage classes of a certain subset being topologically essential, advancing the understanding of preimage class minimization.

Contribution

It introduces new conditions on spaces X and Y that guarantee the homotopic map with all Nielsen preimage classes essential, a novel result in topological fixed point theory.

Findings

Conditions on spaces X, Y and subset B guarantee essential Nielsen preimage classes.

Existence of homotopic maps with all Nielsen classes topologically essential.

Advances in understanding the structure of preimage classes in topology.

Abstract

We find conditions on topological spaces X, Y and nonempty subset B of Y which guarantee that for each continuous map f from X to Y there exists a map g homotopic to f such that Nielsen preimage classes of g^{-1}(B) are all topologically essential.