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Exercise 6| Show complete proof and solution. In R" wheren E N, let B,(x) = {y : ||x – y|| < r} and T = {EC R" : (Vx E E), (3r > 0) such that B,(x) C E} Show using the definition of topology that T is a topology on R".

Exercise 6| Show complete proof and solution. In R" wheren E N, let B,(x) = {y : ||x – y|| < r} and T = {EC R" : (Vx E E), (3r > 0) such that B,(x) C E} Show using the definition of topology that T is a topology on R".

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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Show complete proof/solution.
Exercise 6| Show complete proof and solution. In R" wheren E N, let B,(x) = {y : ||x – y|| < r} and T = {E C R" : (Vx E E), (3r > 0) such that B,(x) C E} Show using the definition of topology that T is a topology on R".
Transcribed Image Text:Exercise 6| Show complete proof and solution. In R" wheren E N, let B,(x) = {y : ||x – y|| < r} and T = {E C R" : (Vx E E), (3r > 0) such that B,(x) C E} Show using the definition of topology that T is a topology on R".
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