Co-Hopf Space Structure on Closure Spaces

Authors : Sibel DEMİRALP

Pages : 321-330

Doi:10.47000/tjmcs.1091039

View : 19 | Download : 12

Publication Date : 2022-12-30

Article Type : Research Paper

Abstract :By constructing Hopf costructures on closure spaces via homotopy, we give the concepts of closure Hopf cospace insert ignore into journalissuearticles values(CH-cospace); and closure Hopf cogroup insert ignore into journalissuearticles values(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 insert ignore into journalissuearticles values($\\mathcal{CHC}$); and the category of groups and homomorphisms.
Keywords : Homotopy, closure space, Hopf cospace