Coincidence theorems for finite topological spaces
DOI:
https://doi.org/10.12775/TMNA.2024.028Keywords
Finite $T_0$-spaces, Alexandroff spaces, posets, multivalued maps, fixed points, dynamical systems, approximation of polyhedraAbstract
In this work, we adapt the definition of the Vietoris map to the setting of finite topological spaces and establish several coincidence theorems. From these theorems, we derive a Lefschetz fixed point theorem for multivalued maps, which extends recent results in the field. Finally, we illustrate an application of this theory in approximating discrete dynamical systems.References
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Copyright (c) 2025 Manuel A. Morón, Pedro J. Chocano, Francisco R. Ruiz del Portal
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