Constancy of upper-continuous two-valued mappings into the Sorgenfrey line

• Date: 2007
• Main Authors: Maslyuchenko, V. K., Fotii, O. H., Маслюченко, В. К., Фотій, О. Г.
• Format: Article
• Language: Ukrainian; English
• Published: Institute of Mathematics, NAS of Ukraine 2007
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/3367
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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.