Co-Hopf Space Structure on Closure Spaces

Year 2022, Volume: 14 Issue: 2, 321 - 330, 30.12.2022

Sibel Demiralp

https://doi.org/10.47000/tjmcs.1091039

Abstract

By constructing Hopf costructures on closure spaces via homotopy, we give the concepts of closure Hopf cospace (CH-cospace) and closure Hopf cogroup (CH-cogroup). We then prove that retract and deformation retract of a CH-cospace are also a CH-cospace. We construct a Hopf costructure on a set with the help of the quotient closure operator. We also show that a closure space with the same homotopy type as a CH-cogroup is itself a CH-cogroup. We prove the existence of a covariant functor between the homotopy category of the pointed closure spaces ($\mathcal{CHC}$) and the category of groups and homomorphisms.

Keywords

Homotopy, closure space, Hopf cospace

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