Year: 2023
Type: preprint
Abstract: The concept of $\mathcal S$-topological $σ$-ideal in measurable space $(X, \mathcal S)$ was introduced by Hejduk and using a theorem of Wagner on convergence of measurable functions characterized $\mathcal S$-topological $σ$-ideals. In this paper, we give a general construction of $\mathcal S$-topological $σ$-ideals from structures induced by $σ$-algebras and weakly upper semicontinuous $ω$-small systems. We also show that instead of weak upper semicontinuity, if we use upper semicontinuity, we get $\mathcal S$-uniformizable $σ$-ideals. This generalizes the approach of Wagner and Wilczynski metrizing Boolean Lattice of measurable functions
Source: arXiv (Cornell University)
Authors: Basu, Sanjib, Sen, Debasish
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4367628268