International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/1335 2020 2020 Department of Mathematics, Faculty of Science, University of Zakho, Zakho 42002, Iraq;Department of Computer Science, College of Science, Cihan University-Duhok, Duhok 42001, Iraq Baravan A. Asaad Department of Mathematics, Faculty of Education, University of Zakho, Zakho 42002, Iraq Sagvan Y. Musa Hypersoft topology (HST) is the study of a structure based on all hypersoft (HS) sets on a given set of alternatives. In continuation of this concern, in this article, we introduce new maps namely HS continuous, HS open, HS closed, and HS homomorphism. We examine the main characteristics of each of these maps. Furthermore, we study HS compact space and discuss some of its properties. We point out that HS compactness preserved under HS continuous map. 2022 2022 19 29 10.54216/IJNS.190202 https://www.americaspg.com/articleinfo/21/show/1335