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

Yutaka Iwamoto

doi:10.4995/agt.2024.20267

Authors

Yutaka Iwamoto National Institute of Technology, Niihama College https://orcid.org/0000-0002-9508-4977

DOI:

https://doi.org/10.4995/agt.2024.20267

Keywords:

uniformly continuous functions, lattice homomorphisms, Higson compactification, Samuel-Smirnov compactification, slowly oscillating functions

Abstract

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.

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Author Biography

Yutaka Iwamoto, National Institute of Technology, Niihama College

Faculty of Fundamental Science

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