Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

The cardinality of quasiconformally nonequivalent topological $ 3$-balls with flat boundaries is $ \mathfrak{c}$


Author: Raimo Näkki
Journal: Proc. Amer. Math. Soc. 75 (1979), 63-68
MSC: Primary 30C60
DOI: https://doi.org/10.1090/S0002-9939-1979-0529214-6
MathSciNet review: 529214
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: The theorem mentioned in the title is proved. During the course of the proof, the failure for $ n = 3$ of the following 2-dimensional result will also be established: The boundary of a Jordan domain D in n-space is a quasiconformal $ (n - 1)$-sphere if every quasiconformal self-mapping of D can be extended to a quasiconformal self-mapping of the whole space.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 30C60

Retrieve articles in all journals with MSC: 30C60


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1979-0529214-6
Keywords: Cardinality, quasiconformal mapping, modulus of a curve family, topological ball, quasiconformal sphere, flat boundary
Article copyright: © Copyright 1979 American Mathematical Society

American Mathematical Society