Abstract
In this paper, we first study the species of finite topological spaces recently considered by Fauvet, Foissy, and Manchon. Then, we construct a twisted pre-Lie structure on the species of connected finite topological spaces. The underlying pre-Lie structure defines a coproduct on the species of finite topological spaces different from those already defined by the authors above. In the end, we illustrate the link between the Grossman–Larson product and the proposed coproduct.
Acknowledgments
I would like to thank my Ph.D. thesis supervisors: Professor Dominique Manchon and Professor Ali Baklouti for their advice, guidance and constant support.