Show that a set A in ℝ2 is open in the Euclidean metric ⇔ it is open in the max metric. Hint: As usual, there are two directions to prove in an ⇔.
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Show that a set A in ℝ2 is open in the Euclidean metric ⇔ it is open in the max metric.
Hint: As usual, there are two directions to prove in an ⇔.
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- Show that a set A in ℝ2 is open in the Euclidean metric ⇔ it is open in the max metric. Hint: As usual, there are two directions to prove in an ⇔.Show that a set A in ℝ2 is open in the Euclidean metric ⇔ it is open in the max metric. There are two directions to prove in an ⇔.Show that a set A in ℝ2 is open in the Euclidean metric ⇔ it is open in the Manhattan metric.Hint: As usual, there are two directions to prove in an ⇔.
- Show that a set A in ℝ2 is open in the Euclidean metric ⇔ it is open in the max metric.Hint: As usual, there are two directions to prove in an ⇔. The picture on p73 of the notes may be somewhat helpful.Show that a set A in ℝ2 is open in the Euclidean metric ⇔ it is open in the Manhattan metric.Prove by sequences that the open balls in R^n with the usual (Euclidean) metric are not compact
- Let (X, d) be a metric space and let A ⊆ X be complete. Show that A is closed.Prove that in a metric space (X, d) every closed ball that is a set K(x, r) = {y e X : d(x, y) <= r}, is closed set. Show on an example that closed ball K(x, r) does not have to be equal a closure of an open ball. signs on the imageB. Given a metric space M with metric d, verify that any ε-ball is an open set.