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Answer the following. Do the best you can entering in mathematical statements into the answer field. 1. State what it means for a set ASR to be open. 2. Explain why an open set A CR can be written as a union of open intervals. 3. Sketch the proof (i.e., don't provide every detail, just explain the main idea) why if f: R → R is continuous and BCR is open, then f-¹(B) is open.

Answer the following. Do the best you can entering in mathematical statements into the answer field. 1. State what it means for a set ASR to be open. 2. Explain why an open set A CR can be written as a union of open intervals. 3. Sketch the proof (i.e., don't provide every detail, just explain the main idea) why if f: R → R is continuous and BCR is open, then f-¹(B) is open.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Answer the following. Do the best you can entering in mathematical statements into the answer field. 1. State what it means for a set ASR to be open. 2. Explain why an open set A CR can be written as a union of open intervals. 3. Sketch the proof (i.e., don't provide every detail, just explain the main idea) why if f: R → R is continuous and BCR is open, then f-¹(B) is open.
Transcribed Image Text:Answer the following. Do the best you can entering in mathematical statements into the answer field. 1. State what it means for a set ASR to be open. 2. Explain why an open set A CR can be written as a union of open intervals. 3. Sketch the proof (i.e., don't provide every detail, just explain the main idea) why if f: R → R is continuous and BCR is open, then f-¹(B) is open.
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