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08 February 2025
 
  » arxiv » 2301.01553

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Non-density of $C^0$-stable mappings on non-compact manifolds
Shunsuke Ichiki ;
Date 4 Jan 2023
AbstractIn 1973, Mather showed that the set of proper $C^0$-stable mappings is dense in the set of all proper mappings, which implies that the set of $C^0$-stable mappings is dense in the set of all mappings if the source manifold is compact. In this paper, we show that the set of $C^0$-stable mappings is never dense in the set of all mappings if the source manifold is non-compact. To prove it, we provide a more essential result by using the notion of topologically critical points.
Source arXiv, 2301.01553
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