Generalized homotopy in generalized topological spaces
الكلمات المفتاحية:
Generalized topology، generalized continuity، homotopy، homotopy equivalenceالملخص
We extend the notion of homotopy between topological spaces to the setting of generalized topological spaces in the sense of Csaszar. We introduce the new notion of generalized homotopy ((u, )-homotopy) between generalized topological spaces and study some of its basic properties.
المراجع
Arkowitz M. (2011). Introduction to homotopy theory, Springer Science & Business Media, New York.
Ayawan, J. B. T., & Canoy Jr, S. R. (2013). Axioms of countability in generalized topological spaces. In: International Mathematical Forum (Vol. 8, No. 31, pp. 1523-1530)
Cs"a" ̀sz"a" ̀r, A. (2002). Generalized topology, generalized continuity, Acta Math. Hungar. 96 351–357.
Cs"a" ̀sz"a" ̀r, A. (2004). Extremally disconnected generalized topologies. In: Annales Univ. Sci. Budapest (Vol. 47, (2004) 91–96).
Cs"a" ̀sz"a" ̀r, A (2005). Generalized open sets in generalized topologies, Acta Math. Hungar., 106, 53-66.
Cs"a" ̀sz"a" ̀r, A. (2009). Products of generalized topologies, Acta Math. Hungar., 123, 127-132.
Cs"a" ̀sz"a" ̀r, A. (2007). Modification of generalized topologies via hereditary classes, Acta Math. Hungar., 115, 29-36
Mukharjee, A. (2020). A covering property with respect to generalized preopen sets, Bol. Soc. Paran. Mat., 38(6), 25-32.
Khodabocus, M. I. & Sookia, N. UL-. H. (2022). Theory of generalized separation axioms in generalized topological spaces, Journal of Universal Mathematics, 5(1), 1-23
Hussain, M., Khan, M. U. D., & Özel, C. (2013). On generalized topological groups, Filomat, 27(4), 567-575.
