arXiv subjects
Publications and source records attributed to Yutaka Iwamoto.
We show that lattice isomorphisms between lattices of slowly oscillating functions on chain-connected proper metric spaces induce coarsely equivalent homeomorphisms. This result leads to a Banach-Stone-like theorem for these lattices. Furthermore, we provide a representation theorem that characterizes linear lattice isomorphisms among these lattices.
We study the space $H(\SO)$ of all homomorphisms of the vector lattice of all slowly oscillating functions on the half-line $\HH=[0,\infty)$. 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 $\HH\times (0, \infty)$. By describing a neighborhood base of zero-homomorphism, we show that $H(\SO)$ is homeomorphic to the space $\HH\times (0, \infty)$ with one point added.
In this paper, we consider spaces whose Higson coronae are indecomposable continua. We show that for a non-compact proper metric space $X$ which is coarsely geodesic and has coarse bounded geometry, the Higson corona of $X$ is an indecomposable continuum if and only if $X$ is coarsely equivalent to the space of natural numbers. Then we give characterizations of finitely generated groups that have one or two ends by decomposability/indecomposability of the components of their Higson coronae. we characterize it as a group whose Higson corona is a topological sum of two indecomposable continua.
In this paper, we study the topological properties of the subpower Higson corona of proper metric spaces and show that the subpower Higson corona of the half open interval with the usual metric is an indecomposable continuum. Some surjective maps from the Higson type coronas onto the Higson type compactifications of the half open interval are also constructed.