Properties of Some Weak Forms of Continuity

As weak forms of continuity in topological spaces, weak continuity [I], quasi continuity [2], semi continuity [3] and almost continuity in the sense of Husain [4] are well-known. Recently, the following four weak forms of continuity have been introduced: weak quasi continuity [5], faint continuity [6], subweak continuity [7] and almost weak continuity [8]. These four weak forms of continuity are all weaker than weak continuity. In this paper we show that these four forms of continuity are respectively independent and investigate many fundamental properties of these four weak forms of continuity by comparing those of weak continuity, semi continuity and almost continuity.