Homomorphisms of the lattice of slowly oscillating functions on the half-line

• Iwamoto, Yutaka ^[1]
  1. [1] National Institute Of Technology

     National Institute Of Technology

     Japón

     
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 25, Nº. 1, 2024, págs. 57-70
• Idioma: inglés
• DOI: 10.4995/agt.2024.20267
• Enlaces
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• Resumen

  • We study the space H(SO) of all homomorphisms of the vector lattice of all slowly oscillating functions on the half-line ℍ = [ 0 , ∞ ) . In contrast to the case of homomorphisms of uniformly continuous functions, it is shown that a homomorphism in H(SO) which maps the unit to zero must be zero-homomorphism. Consequently, we show that the space H(SO) without zero-homomorphism is homeomorphic to ℍ x (0, ∞). By describing a neighborhood base of zero-homomorphism, we show that H(SO) is homeomorphic to the space ℍ x (0, ∞) with one point added.

• Referencias bibliográficas
  • F. Cabello Sánchez, Fine structure of the homomorphisms of the lattice of uniformly continuous functions on the line, Positivity 24, no. 2...
  • F. Cabello Sánchez, and J. Cabello Sánchez, Quiz your maths: Do the uniformly continuous functions on the line form a ring?, Proceedings of...
  • R. Engelking, General topology, Second edition. Sigma Series in Pure Mathematics, 6. Heldermann Verlag, Berlin, 1989.
  • M. I. Garrido, and J. A. Jaramillo, Homomorphisms on function lattices, Monatsh. Math. 141, no. 2 (2004), 127-146. https://doi.org/10.1007/s00605-002-0011-4
  • Y. Iwamoto, Indecomposable continua as Higson coronae, Topology Appl. 283 (2020), Paper no. 107334. https://doi.org/10.1016/j.topol.2020.107334
  • J. Keesling, The one-dimensional Čech cohomology of the Higson compactification and its corona, Topology Proc. 19 (1994), 129-148. https://doi.org/10.1080/0022250X.1994.9990139
  • J. R. Porter, and R. G. Woods, Extensions and absolutes of Hausdorff spaces, Springer-Verlag, New York, 1988. https://doi.org/10.1007/978-1-4612-3712-9
  • J. Roe, Lectures on coarse geometry, University Lecture Series, 31. American Mathematical Society, Providence, RI, 2003. https://doi.org/10.1090/ulect/031
  • R. G. Woods, The minimum uniform compactification of a metric spaces, Fund. Math. 147, no. 1 (1995), 39-59. https://doi.org/10.4064/fm-147-1-39-59