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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