Topometric spaces and perturbations of metric structures
| dc.creator | Yaacov, Itaï Ben | |
| dc.date | 2008-02-26 | |
| dc.date | 2008-06-02 | |
| dc.date.accessioned | 2026-07-07T12:35:45Z | |
| dc.date.available | 2026-07-07T12:35:45Z | |
| dc.description | We develop the general theory of \emph{topometric spaces}, i.e., topological spaces equipped with a well-behaved lower semi-continuous metric function. Spaces of global and local types in continuous logic are the motivating examples for the study of such spaces. In particular, we develop a theory of Cantor-Bendixson analysis of topometric spaces, which can serve as a basis for the study of local stability (extending the \textit{ad hoc} development from \cite{BenYaacov-Usvyatsov:CFO}), as well as of global $\aleph_0$-stability. We conclude with a study of perturbation systems (see \cite{BenYaacov:Perturbations}) in the formalism of topometric spaces. In particular, we show how the abstract development applies to $\aleph_0$-stability up to perturbation. | |
| dc.identifier | https://arxiv.org/abs/0802.4458 | |
| dc.identifier | http://arxiv.org/abs/0802.4458 | |
| dc.identifier | Logic and Analysis 1, 3-4 (2008) 235-272 | |
| dc.identifier | doi:10.1007/s11813-008-0009-x | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/217867 | |
| dc.subject | Logic | |
| dc.title | Topometric spaces and perturbations of metric structures | |
| dc.type | text |