Complexity of global semianalytic sets in a real analytic manifold of dimension 2
Let X subset of R-n be a real analytic manifold of dimension 2. We study the stability index of X, s(X), that is the smallest integer s such that any basic open subset of X can be written using s global analytic functions. We show that s(X) = 2 as it happens in the semialgebraic case. Also, we prove...
| Autores: | , |
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| Tipo de documento: | artigo |
| Data de publicação: | 2001 |
| País: | España |
| Recursos: | Universidad Complutense de Madrid (UCM) |
| Repositório: | Docta Complutense |
| Idioma: | inglês |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/57153 |
| Acesso em linha: | https://hdl.handle.net/20.500.14352/57153 |
| Access Level: | Acceso aberto |
| Palavra-chave: | 512.7 Geometria algebraica 1201.01 Geometría Algebraica |
| Resumo: | Let X subset of R-n be a real analytic manifold of dimension 2. We study the stability index of X, s(X), that is the smallest integer s such that any basic open subset of X can be written using s global analytic functions. We show that s(X) = 2 as it happens in the semialgebraic case. Also, we prove that the Hormander-Lojasiewicz inequality and the Finiteness Theorem hold true in this context. Finally, we compute the stability index for basic closed subsets, S, and the invariants t and (t) over bar for the number of unions of open (resp. closed) basic sets required to describe any open (resp. closed) global semianalytic set. |
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