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In 2008, M. Caldas and G. Navalagi introduced a new class of generalized open functions called weakly -open functions. By introducing a new type of open functions called relatively weakly -open together with weakly -open functions, we establish a new decomposition of -open functions. 2010 Mathematics Subject Classification. 54A40, 54C10, 54D10; Secondary: 54C08
Caldas et al. (Tue,) studied this question.