ON I-COMPACT SUBSETS AND IC-CONTINUOUS FUNCTIONS

The concept of compactness modulo an ideal was first introduced by Newcomb in 1967 and investigated by Hamlett, Rose, and Jankovic in 1990. In this paper we give some new characterizations and properties of I-compact subsets. By using this notion, we introduce a new class of functions, called IC-continuous functions, which contains the class of continuity and is contained in the class of H-continuity. Some characterizations and several properties of this new type of function are presented. Relationships between IC-continuity and other corresponding notions are studied.