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

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Abstract

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.

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References

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Author information

Correspondence to V. K. Maslyuchenko.

Additional information

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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 8, pp. 1034–1039, August, 2007.

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Maslyuchenko, V.K., Fotii, O.H. Constancy of upper-continuous two-valued mappings into the Sorgenfrey line. Ukr Math J 59, 1148–1154 (2007). https://doi.org/10.1007/s11253-007-0076-2

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Keywords

  • Topological Space
  • Compact Subset
  • Topological Structure
  • Neighborhood Versus
  • Multivalued Mapping