Suppose di and d2 are metrics on a set S. Suppose d1 generates the topology T1 = {A, Ø, S, B} and d2 generates the topology T2 = {C,Ø, S, D}. Make a statement in terms of the elements of n and T2 that will make di equivalent to d2.

Answered: Suppose di and d2 are metrics on a set…

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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Suppose di and d2 are metrics on a set S. Suppose d1 generates the topology T1 = {A, Ø, S, B} and d2 generates the topology T2 = {C,
Ø, S, D}. Make a statement in terms of the elements of n and T2 that will make di equivalent to d2.

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We are given that $d_{1}$ and $d_{2}$ are metrics on a set S. Further, $d_{1}$ generates the topology $τ_{1} = \{\begin{matrix} A, & φ, & S, & B \end{matrix}\}$ and $d_{2}$ generates the topology $τ_{2} = \{\begin{matrix} C, & φ, & S, & D \end{matrix}\}$ .

Here, we need to make a statement in terms of the elements of $τ_{1}$ and $τ_{2}$ that will make $d_{1}$ equivalent to $d_{2}$ .

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