Question 3. An open and connected subset of C is called a domain. (a) Using the definitions (of open sets and connected sets), prove that if D₁, D₂ C C are domains and D₁ D₂ ‡ Ø, then D₁ U D₂ is also a domain. (b) Given an example to the following fact: D₁ D₂ is not necessarily a domain even if D₁, D2 are both domains.
Question 3. An open and connected subset of C is called a domain. (a) Using the definitions (of open sets and connected sets), prove that if D₁, D₂ C C are domains and D₁ D₂ ‡ Ø, then D₁ U D₂ is also a domain. (b) Given an example to the following fact: D₁ D₂ is not necessarily a domain even if D₁, D2 are both domains.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.4: Binary Operations
Problem 9E: 9. The definition of an even integer was stated in Section 1.2. Prove or disprove that the set of...
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Transcribed Image Text:Question 3. An open and connected subset of C is called a domain.
(a) Using the definitions (of open sets and connected sets), prove that if D₁, D₂ C C
are domains and D₁ D₂ ‡ Ø, then D₁ U D₂ is also a domain.
(b) Given an example to the following fact: D₁ D₂ is not necessarily a domain
even if D₁, D2 are both domains.
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