For the metric space $ (\mathbb{R}, d) $ with $ d $ the usual Euclidean metric, which sets are in the topology $\tau$ generated by $d$? Explain.i). $ \mathbb{R} $ii). $ (1, 2] $iii). $ \text{Int}(1, 2] $

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Answered: For the metric space (R, d) with d the…

For the metric space (R, d) with d the usual Euclidean metric, which sets are in the topology T generated by d? Explain. i). IR ii). (1, 2] iii). Int(1,2]

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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Question

For the metric space $ (\mathbb{R}, d) $ with $ d $ the usual Euclidean metric, which sets are in the topology $\tau$ generated by $d$? Explain.

i). $ \mathbb{R} $

ii). $ (1, 2] $

iii). $ \text{Int}(1, 2] $

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