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let X=(0,1) and U subscript n =(1/n,1) (n>=2). Does a lebesgue number exist for the cover { U subscript n : n>=2}}

Question

let X=(0,1) and U subscript n =(1/n,1) (n>=2). Does a lebesgue number exist for the cover { U subscript n : n>=2}}
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Solution 1

Yes, a Lebesgue number does exist for the cover {U_n : n>=2} of the set X=(0,1).

Here's the step-by-step explanation:

  1. The Lebesgue number of an open cover of a metric space is a positive number δ such that every subset of the space of diameter < δ is contained in some member of the cover.

  2. Knowee AI is a powerful AI-powered study tool designed to help you to solve study problem.

Knowee AI  is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI  is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI  is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI  is a powerful AI-powered study tool designed to help you to solve study problem.
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