Summary
Noiri 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.
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Ekici, E. Generalization of perfectly continuous, regular set-connected and clopen functions. Acta Math Hung 107, 193–206 (2005). https://doi.org/10.1007/s10474-005-0190-2
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DOI: https://doi.org/10.1007/s10474-005-0190-2