PurposeIn 2005, Smarandache generalized the Atanassov's intuitionistic fuzzy sets (IFSs) to neutrosophic sets (NS), and other researchers introduced the notion of interval neutrosophic set (INSs), which is an instance of NS, and studied various properties. The notion of neutrosophic topology on the non‐standard interval is also due to Smarandache. The purpose of this paper is to study relations between INSs and topology.Design/methodology/approachThe paper investigates the possible relations between INSs and topology.FindingsRelations on INSs and neutrosophic topology.Research limitations/implicationsClearly, the paper is confined to IFSs and NSs.Practical implicationsThe main applications are in the mathematical field.Originality/valueThe paper shows original results on fuzzy sets and topology.