Constancy of upper-continuous two-valued mappings into the Sorgenfrey line - Maslyuchenko, V. K.; Fotii, O. H. (Ukrains’kyi Matematychnyi Zhurnal, 2007)
By using the Sierpiński continuum theorem, we prove that every upper-continuous two-valued mapping of a linearly connected space (or even a c-connected space, i.e., a space in which any two points can be connected by a continuum) into the Sorgenfrey line is necessarily constant.