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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.

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter7: Locus And Concurrence
Section7.2: Concurrence Of Lines
Problem 7E: Which lines or line segments or rays must be drawn or constructed in a triangle to locate its a...
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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.
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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