Constancy of upper-continuous two-valued mappings into the Sorgenfrey line
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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.
KeywordsTopological Space Compact Subset Topological Structure Neighborhood Versus Multivalued Mapping
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