Ekici, E2025-01-272025-01-2720050236-5294https://doi.org/10.1007/s10474-005-0190-2https://hdl.handle.net/20.500.12428/22021Noiri in 1984, Dontchev, Ganster and Reilly in recent years and Reilly and Vamanamurthy in 1983 introduced the notion of perfectly continuous, regular set-connected and clopen functions, respectively. The aim of this paper is to introduce the notion of a new class of functions which is called almost clopen functions including the classes of perfectly continuous, regular set-connected and clopen functions. Furthermore, properties of almost clopen functions are obtained and relationships among almost clopenness, perfect continuity, regular set-connectedness, clopenness and almost continuity are investigated.eninfo:eu-repo/semantics/closedAccessregular openclopenalmost clopenregular set-connectedperfect continuityclopen almost closed graphsArticle107319320610.1007/s10474-005-0190-2Q4WOS:0002293281000032-s2.0-17744378406Q2