Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5778113 | Annals of Pure and Applied Logic | 2017 | 7 Pages |
Abstract
Continuous extension cells, or CE-cells, are cells whose defining functions have continuous extensions on closure of their domains. An o-minimal structure has the CE-cell decomposition property if any cell decomposition has a refinement by CE-cells. If the o-minimal structure M has the CE-cell decomposition property, then it has the open cell property. In other words, every definable open set in M is a finite union of definable open cells. Here, we show that the open cell property does not imply the CE-cell decomposition property. Also, after introducing an existence of limit property, we show that the CE-cell decomposition property is equivalent to the open cell property and the existence of limit property.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Logic
Authors
Somayyeh Tari,