Abstract
Our main purpose in this chapter is to show that Theorems 6.36 and 6.37 remain true even if we replace the assumption of finite connectivity of the components of \( {mathbb{S}^2}\backslash C\,(F,\,\overline Y ) \) by the weaker assumption that each of these components be countably connected. We shall do this by an inductive method, starting with finite connectivity of a component Ω of \( {mathbb{S}^2}\backslash C\,(F,\,\overline Y ) \), and then allowing the family of components of \( {mathbb{S}^2}\backslash \,\Omega \) to become more and more complicated.
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© 1974 Springer-Verlag Berlin · Heidelberg
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Beck, A. (1974). Existence Theorems II. In: Continuous Flows in the Plane. Die Grundlehren der mathematischen Wissenschaften, vol 201. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-65548-7_8
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DOI: https://doi.org/10.1007/978-3-642-65548-7_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-65550-0
Online ISBN: 978-3-642-65548-7
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