Question

Prove that if A is open and B is closed then A - B is open. (Hint: Use Theorems 3.2.3 and 3.2.13 from the textbook.) Theorem 3.2.3. (i) The union of an arbitrary collection of open sets is open. (ii) The intersection of a finite collection of open sets is open. Theorem 3.2.13. A set O is open if and only if Oc is closed. Likewise, a set F is closed if and only if Fc is open.

          Prove that if A is open and B is closed then A - B is open.
(Hint: Use Theorems 3.2.3 and 3.2.13 from the textbook.)
Theorem 3.2.3. (i) The union of an arbitrary collection of open sets is open.
(ii) The intersection of a finite collection of open sets is open.
Theorem 3.2.13. A set O is open if and only if Oc is closed. Likewise, a set F is closed if and only if Fc is open.

Prove that if A is open and B is closed then A - B is open.
(Hint: Use Theorems 3.2.3 and 3.2.13 from the textbook.)
Theorem 3.2.3. (i) The union of an arbitrary collection of open sets is open.
(ii) The intersection of a finite collection of open sets is open.
Theorem 3.2.13. A set O is open if and only if Oc is closed. Likewise, a set F is closed if and only if Fc is open.

Added by Pablo C.

Calculus

Laura Taalman, Peter Kohn 1st Edition

Chapter 12

Instant Answer

Solved by Expert Sri K

09/21/2023

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Prove that if A is open and B is closed then A - B is open. (Hint: Use Theorems 3.2.3 and 3.2.13 from the textbook.) Theorem 3.2.3. (i) The union of an arbitrary collection of open sets is open. (ii) The intersection of a finite collection of open sets is open. Theorem 3.2.13. A set O is open if and only if Oc is closed. Likewise, a set F is closed if and only if Fc is open.