Constancy of upper-continuous two-valued mappings into the Sorgenfrey line
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.
English version (Springer): Ukrainian Mathematical Journal 59 (2007), no. 8, pp 1148-1154.
Citation Example: Fotii O. H., Maslyuchenko V. K. Constancy of upper-continuous two-valued mappings into the Sorgenfrey line // Ukr. Mat. Zh. - 2007. - 59, № 8. - pp. 1034–1039.