Parameterized stratification and piece number of D-semianalytic sets
| dc.creator | Celikler, Y. Firat | |
| dc.date | 2004-09-07 | |
| dc.date.accessioned | 2026-07-07T05:11:51Z | |
| dc.date.available | 2026-07-07T05:11:51Z | |
| dc.description | We obtain results on the geometry of D-semianalytic and subanalytic subsets over a complete, non-trivially valued non-Archimedean field K, which is not necessarily algebraically closed. Among the results are a parameterized smooth stratification theorem and several results concerning the dimension of the D-semianalytic and subanalytic sets. We also extend Bartenwerfer's definition of piece number for analytic K-varieties to D-semianalytic sets and prove the existence of a uniform bound for the piece number of the fibers of a D-semianalytic set. We also establish a connection between the piece number and complexity of D-semianalytic sets which are subsets of the line and thereby give a simpler proof of the Complexity Theorem of Lipshitz and Robinson. We finish by proving that for each D-semianalytic X, there is a semialgebraic Y such that one dimensional fibers of X are among the one dimensional fibers of Y. This is an analogue of a theorem by van den Dries, Haskell and Macpherson. | |
| dc.description | 25 pages | |
| dc.identifier | https://arxiv.org/abs/math/0409095 | |
| dc.identifier | http://arxiv.org/abs/math/0409095 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/72385 | |
| dc.subject | Logic | |
| dc.title | Parameterized stratification and piece number of D-semianalytic sets | |
| dc.type | text |