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Article overview
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Non-density of $C^0$-stable mappings on non-compact manifolds | Shunsuke Ichiki
; | Date: |
4 Jan 2023 | Abstract: | In 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 | Services: | Forum | Review | PDF | Favorites |
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