Compact mappings and <i>s</i>-mappings at subsets

Abstract Almost s s -mappings and almost compact mappings have been introduced studied. In this article, we continue to research some questions related the -images (resp., images) of metric spaces. The following results are obtained. (1) A space X X is a quotient image if only sequential having c ∗ c{s}^{\ast } -network which point-regular at nonisolated points, gives an affirmative answer Question 4.9 in article “S. Lin, X. W. Ling, Y. Ge, Point-regular covers sequence-covering , Topology Appl. 271 (2020), 106987.” (2) There exists bi-quotient satisfying no base, point-countable negative answers 3.1 “X. Ling S. On open s-images spaces Adv. Math. (China) 48 (2019), no. 4, 489–496” 3.7 He, Point-countable s-mappings subsets 290 (2021), 107572.” (3) Some characterizations countably pseudo-open