On feebly monotone and related classes of mappings
A mapping between continua is said to be feebly monotone provided whenever the range is the union of two proper subcontinua, their preimages are connected. These mappings and their relations to monotone, almost monotone, quasi-monotone, and weakly monotone mappings are studied. Further, the author investigates special properties of continua in relation to these various classes of mappings. Results of \textit{J. B. Fugate} and \textit{L. Mohler} [Colloq. Math. 28, 221-224 (1973; Zbl 0277.54006)] and \textit{T. Maćkowiak} [Bull. Acad. Pol. Sci., Sér. Sci. Math. Astron. Phys. 24, 335-339 (1976; Zbl 0337.54019)] on the invariance of irreducibility of continua, known for quasi-monotone mappings, are extended to feebly monotone mappings. Relations between unicoherence of continua and feebly monotone mappings are established and previous results of the author's concerning terminal subcontinua, in the sense of \textit{D. E. Bennett} and \textit{J. B. Fugate} [Continua and their non-separating subcontinua, Diss. Math. 149 (1977; Zbl 0354.54017)] are extended.
scientific article; zbMATH DE number 1475347