arXiv
Open Access
2021
On definable open continuous mappings
Si Tiep Dinh
Tien Son Pham
Abstrak
For a definable continuous mapping $f$ from a definable connected open subset $Ω$ of $\mathbb R^n$ into $\mathbb R^n,$ we show that the following statements are equivalent: (i) The mapping $f$ is open. (ii) The fibers of $f$ are finite and the Jacobian of $f$ does not change sign on the set of points at which $f$ is differentiable. (iii) The fibers of ${f}$ are finite and the set of points at which $f$ is not a local homeomorphism has dimension at most $n - 2.$ As an application, we prove that Whyburn's conjecture is true for definable mappings: A definable open continuous mapping of one closed ball into another which maps boundary homeomorphically onto boundary is necessarily a homeomorphism.
Topik & Kata Kunci
Penulis (2)
S
Si Tiep Dinh
T
Tien Son Pham
Akses Cepat
Informasi Jurnal
- Tahun Terbit
- 2021
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- en
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- arXiv
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