Resumen:
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Let M be a real analytic manifold and O(M) its ring of global analytic functions. Let Z be a global semianalytic set of M (that is, a subset of M of the form Z=?r i=0{x?M:fi1 (x)>0,?,fis (x)>0, gi (x)=0}, where fij,gi?O(M)). In this paper, the author proves the following three theorems. Theorem: If cl(Z)?Z[resp. Z?int(Z)] is relatively compact, then the closure cl(Z)[resp. int(Z)] of Z is also a global semianalytic set. Theorem: If Z is closed [resp. open] and Z?int(Z)[resp. cl(Z)?Z] is compact, then there are analytic functions fij?O(M) such that Z=?r i=1{x?M:fi1 (x)?0,?,fis (x)?0}[resp. Z=?r i=1{x?M:fi1 (x)>0,?,fis(x)>0}]. Theorem: If cl(Z)?Z is relatively compact, then the connected components of Z are also global semianalytic sets.
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