Co-Hopf Space Structure on Closure Spaces

Autor:	Sibel DEMİRALP
Rok vydání:	2022
Předmět:	Matematik General Earth and Planetary Sciences Homotopy closure space Hopf cospace Mathematics General Environmental Science
Zdroj:	Volume: 14, Issue: 2 321-330 Turkish Journal of Mathematics and Computer Science
ISSN:	2148-1830
DOI:	10.47000/tjmcs.1091039
Popis:	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.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d10ef93c57ef660839773bae8f6e326c https://doi.org/10.47000/tjmcs.1091039 Zobrazit plný text záznamu