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1. Rudin Chapter 7 Exercise 1. (Note: Given sequence of functions fn : X → Y , the sequence is uniformly bounded if there exist M > 0 so that |fn(x)| ≤ M for all n and x ∈ X.)
2. Rudin Chapter 7 Exercise 2 3. Rudin Chapter 7 Exercise 3 4. Rudin Chapter 7 Exercise 4 5. Rudin Chapter 7 Exercise 5 6. Rudin Chapter 7 Exercise 6 7. Rudin Chapter 7 Exercise 7
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Functions satisfying the condition in Problem 6 on its domain is said to be H¨ older continuous with exponent α.
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Solution: Intuitively, if γ does not intersect negative real axis, it can never travel a complete loop and therefore the winding number has to be 06. However, since the expression
Functions satisfying the condition in Problem 6 on its domain is said to be H¨ older continuous with exponent α..
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