Halgwrd Mohammed Darwesh^{1, a} And Shagull Hossein Mahmood^{2, b}

^1,2 Department of Mathematics, College of Science, University of Sulaimani,

46001 Sulaimani, Kurdistan Region, Iraq

^a) halgwrd.darwesh@univsul.edu.iq
^b) shagull.mahmmod@univsul.edu.iq

In this 𝑤𝑜𝑟𝑘, we study and define two new concepts of functions named  and  functions by using the concepts of  and ϲ𝑙𝑜𝑠𝑒𝑑 sets. The concept of  function strictly located between both the concepts of  and  functions. We obtain a few properties of these functions, however, the connections between them are examined.