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Pseudo definably connected definable sets
Author(s) -
Eivazloo Jafar S.,
Tari Somayyeh
Publication year - 2016
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.201400034
Subject(s) - social connectedness , mathematics , set (abstract data type) , simply connected space , pure mathematics , topology (electrical circuits) , combinatorics , computer science , psychology , psychotherapist , programming language
In o‐minimal structures, every cell is definably connected and every definable set is a finite union of its definably connected components. In this note, we introduce pseudo definably connected definable sets in weakly o‐minimal structures having strong cell decomposition, and prove that every strong cell in those structures is pseudo definably connected. It follows that every definable set can be written as a finite union of its pseudo definably connected components. We also show that the projections of pseudo definably connected definable sets are pseudo definably connected. Finally, we compare pseudo definable connectedness with (recently introduced) weak definable connectedness of definable sets in weakly o‐minimal structures.