Some (Lambda,b)-type mappings in topological spaces

Abstract

We introduce and study (Lambda, b)-continuous, (Lambda, b)-irresolute and quasi-(Lambda, b)-irresolute mappings. Some characterizations and several properties concerning aforesaid mappings are obtained. The authors also introduce (Lambda, b)-compactness and (\Lambda, b)-connectedness. It is proved that (Lambda, b)-compactness (respectively (\Lambda, b)-connectedness) is preserved under (\Lambda, b)-irresolute mappings. The paper also touches the topics frontier points, Dirichlet's function, filter and algebraic structure of some functions.