Submission date: 3 April 2019. PAPER WITHDRAWN, 26 APRIL 2020

Abstract:

Let G be a definably compact definable C^r group. We prove that if X is a non-definably compact affine definable C^r G manifold and X_1, ..., X_n are non-definably compact definable C^r G submanifolds of X in general position such that (X; X_1, ..., X_n) satisfies the frontier condition, then (X; X_1, ..., X_n) is simultaneously definably C^r G compactifiable.

Mathematics Subject Classification: 14P10, 14P20, 58A05, 03C64.

Keywords and phrases: definable C^r G manifolds, simultaneous definable C^r G compactifications, simultaneous definable C^r G approximations.

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