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





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


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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How to Cite

Y. Iwamoto, “Homomorphisms of the lattice of slowly oscillating functions on the half-line”, Appl. Gen. Topol., vol. 25, no. 1, pp. 57–70, Apr. 2024.



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