On upper and lower β-continuous multifunctions

Abstract

In this paper the authors define a multifunction \(F:X \mapsto Y\) to be upper (respectively, lower) \(\beta\)-continuous if \(F^+(V)\) (resp. \(F^-(V))\) is \(\beta\)-open in \(X\) for every open set \(V\) of \(Y\). They obtain some characterizations and several properties concerning upper (resp. lower) \(\beta\)-continuous multifunctions. The relationships between these multifunctions and quasi continuous multifunctions are investigated.