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Rigid Subanalytic Subsets of Curves and Surfaces
Author(s) -
Lipshitz Leonard,
Robinson Zachary
Publication year - 1999
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610799007358
Subject(s) - algebraically closed field , zero (linguistics) , mathematics , set (abstract data type) , field (mathematics) , pure mathematics , combinatorics , computer science , philosophy , linguistics , programming language
Working over an algebraically closed, complete, non‐Archimedean, nontrivially valued field of characteristic zero, it is shown that (i) any subanalytic subset of a one‐dimensional semialgebraic set is semialgebraic, (ii) any one‐dimensional subanalytic set is semianalytic, and (iii) any subanalytic subset of a two‐dimensional semianalytic set is semianalytic.