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Near-selection theorems for C-spaces

Volume 169 / 2022

Valentin Gutev Colloquium Mathematicum 169 (2022), 171-187 MSC: 54C60, 54C65, 54D20, 54F45, 55M10, 55U10. DOI: 10.4064/cm8319-6-2021 Published online: 31 January 2022


Haver’s near-selection theorem deals with approximate selections of Hausdorff continuous CE-valued mappings defined on $\sigma $-compact metrizable $C$-spaces. In the present paper, we show that it is valid for all paracompact $C$-spaces, which answers in the affirmative a question raised by V. Valov. The technique developed to achieve this result is based on oriented simplicial complexes. It makes not only a considerable simplification in the proof but is also successful in generalising an alternative near-selection theorem for compact metric $C$-spaces to all paracompact finite $C$-spaces.


  • Valentin GutevDepartment of Mathematics
    Faculty of Science
    University of Malta
    Msida MSD 2080, Malta

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