Turkish Journal of Mathematics and Computer Science

Yazarlar: ["Sibel DEMİRALP"]

Konular:-

DOI:10.47000/tjmcs.1091039

Anahtar Kelimeler:Homotopy,Closure space,Hopf cospace

Özet: 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.

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