and where x=0 is the origin.
.
defined by setting
.
Mathematics Homework Solutions
#52465
Metrics, Epsilon Balls and Bounded Functions
Describe the ε-balls centered at an arbitrary point for this metric and draw a picture of in he special case of and where x=0 is the origin.
Let be the set of al bounded functions where a function is called bounded if there exists a positive real number K such that for all .
Prove that the function defined by setting
defines a metric on the set .
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Metrics, Epsilon Balls and Bounded Functions are investigated. The solution is detailed and well presented.
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