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Comultiplications on the Localized Spheres and Moore Spaces

Author

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  • Dae-Woong Lee

    (Department of Mathematics, and Institute of Pure and Applied Mathematics, Jeonbuk National University, 567 Baekje-daero, Deokjin-gu, Jeonju-si, Jeollabuk-do 54896, Korea)

Abstract

Any nilpotent CW-space can be localized at primes in a similar way to the localization of a ring at a prime number. For a collection P of prime numbers which may be empty and a localization X P of a nilpotent CW-space X at P , we let | C ( X ) | and | C ( X P ) | be the cardinalities of the sets of all homotopy comultiplications on X and X P , respectively. In this paper, we show that if | C ( X ) | is finite, then | C ( X ) | ≥ | C ( X P ) | , and if | C ( X ) | is infinite, then | C ( X ) | = | C ( X P ) | , where X is the k -fold wedge sum ⋁ i = 1 k S n i or Moore spaces M ( G , n ) . Moreover, we provide examples to concretely determine the cardinality of homotopy comultiplications on the k -fold wedge sum of spheres, Moore spaces, and their localizations.

Suggested Citation

  • Dae-Woong Lee, 2020. "Comultiplications on the Localized Spheres and Moore Spaces," Mathematics, MDPI, vol. 8(1), pages 1-19, January.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:1:p:86-:d:305295
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    Cited by:

    1. Sunyoung Lee & Dae-Woong Lee, 2020. "Coalgebras on Digital Images," Mathematics, MDPI, vol. 8(11), pages 1-21, November.
    2. Dae-Woong Lee, 2020. "On the Digital Cohomology Modules," Mathematics, MDPI, vol. 8(9), pages 1-21, August.

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