Induced mappings on n – symmetric product hyperspace

Abstract

Recently, the class of continuous functions between hyperspaces has been extensively studied by many authors (see [1-9]). Researchers have focused on analyzing important properties of continuous functions and the relationship between a mapping  and its corresponding induced mapping  on the -th symmetric product hyperspace. In this paper, we prove that  can be derived from  if  represents classes of continuous functions such as open, semi-open, closed, and quasi-open functions. We also identify the necessary and sufficient conditions under which  implies  for other classes of continuous functions, such as open, induced open, and semi-open functions. Additionally, we examine the impact of these transformations on the mathematical structure of hyperspaces and the connection between continuous mappings.