On feebly monotone and related classes of mappings

A mapping between continua is said to be feebly monotone if whenever the range is the union of two proper subcontinua, their preimages are connected. Basic properties of these mappings and their connections with related classes of mappings are investigated. Further, some special properties of continua as indecomposability, irreducibility, unicoherence, and some other are studied when applied to either the domain or the range of the considered mapping. Finally terminal subcontinua and related concepts are discussed pertinent to feebly monotone mappings.