Isn-sequential spaces and the images of metric spaces

In this paper we introduce and study Isn-sequential spaces and I-snf-countable spaces. The following main results are obtained: let I be an ideal on N and X be a topological space, then (1) X is an Isn-sequential space if and only if each Isn-continuous (resp. quotient) mapping on the space X is continuous (resp. Isn-quotient). (2) X is an I -neighborhood space if and only if each Isn-quotient mapping on the space X is I -quotient, which answers [10, Question 4.12(2)] in the affirmative. (3) X is an I-snf-countable space if and only if X is a continuous and 1 -I -covering image of a metric space. (4) If I is a K-uniform ideal on N, then each topological space is an I -neighborhood space.(c) 2023 Elsevier B.V. All rights reserved.