2. Is R bounded with respect to this metric? 3. Compare the open balls B(0,2), B(0,4), and B(1, 4). What do you observe? 4. Show that is not equivalent to the usual metric space on R. 5. Is & topologically equivalent to the usual metric space on R. 6. Show that Ris not sequentially compact with respect to the metric 6. 7. Deduce.
2. Is R bounded with respect to this metric? 3. Compare the open balls B(0,2), B(0,4), and B(1, 4). What do you observe? 4. Show that is not equivalent to the usual metric space on R. 5. Is & topologically equivalent to the usual metric space on R. 6. Show that Ris not sequentially compact with respect to the metric 6. 7. Deduce.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
topology part 5 6 7
![Exercise 1. Let z ad y be two reals. Set for zand y,
6(x, y) |tan ¹r - tan-¹ y.
1. Show that is a metric on R.
2. Is R bounded with respect to this metric?
3. Compare the open balls B(0,2), B(0,4), and B(1,4). What do you observe?
4. Show that is not equivalent to the usual metric space on R.
5. Is á topologically equivalent to the usual metric space on R.
6. Show that R is not sequentially compact with respect to the metric 6.
7. Deduce.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8765329c-fafe-4a03-a485-f0c3c6508324%2F568f5bef-f53c-4332-9a76-86f44dc4d7f9%2F2bueqcb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Exercise 1. Let z ad y be two reals. Set for zand y,
6(x, y) |tan ¹r - tan-¹ y.
1. Show that is a metric on R.
2. Is R bounded with respect to this metric?
3. Compare the open balls B(0,2), B(0,4), and B(1,4). What do you observe?
4. Show that is not equivalent to the usual metric space on R.
5. Is á topologically equivalent to the usual metric space on R.
6. Show that R is not sequentially compact with respect to the metric 6.
7. Deduce.
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