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

Autor:	Yutaka Iwamoto
Jazyk:	angličtina
Rok vydání:	2024
Předmět:	uniformly continuous functions lattice homomorphisms higson compactification samuel-smirnov compactification slowly oscillating functions Mathematics QA1-939 Analysis QA299.6-433
Zdroj:	Applied General Topology, Vol 25, Iss 1, Pp 57-70 (2024)
Druh dokumentu:	article
ISSN:	1576-9402 1989-4147
DOI:	10.4995/agt.2024.20267
Popis:	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.
Databáze:	Directory of Open Access Journals
Externí odkaz:	https://doaj.org/article/b2f664acfbfa4e61b137971615564142 Zobrazit plný text záznamu View record in DOAJ Plný text ve formátu PDF