TY - JOUR
AU - Iwamoto, Yutaka
PY - 2024/04/02
Y2 - 2024/11/10
TI - Homomorphisms of the lattice of slowly oscillating functions on the half-line
JF - Applied General Topology
JA - Appl. Gen. Topol.
VL - 25
IS - 1
SE -
DO - 10.4995/agt.2024.20267
UR - https://polipapers.upv.es/index.php/AGT/article/view/20267
SP - 57-70
AB - <div><div>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.</div></div>
ER -