- Turkish Journal of Mathematics and Computer Science
- Vol: 14 Issue: 2
- Co-Hopf Space Structure on Closure Spaces
Co-Hopf Space Structure on Closure Spaces
Authors : Sibel DEMİRALP
Pages : 321-330
Doi:10.47000/tjmcs.1091039
View : 5 | Download : 2
Publication Date : 2022-12-30
Article Type : Research
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