Let n ∈ N. Give an example of a region U ⊂ C whose complement in C has n connected components but whose complement in C̅ has only one connected component. In particular, U is simply connected. C̅ in here is the Riemann sphere.

Let n ∈ N. Give an example of a region U ⊂ C whose complement in C has n connected components but whose complement in C̅ has only one connected component. In particular, U is simply connected. C̅ in here is the Riemann sphere.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter6: More On Rings

Section6.2: Ring Homomorphisms

Problem 6E

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