5 See below picture:Let O denote the collection of all open subsets of the real line R. Provethat there is a smallest o-algebra B such that O C B. (By saying Bis the smallest 0-algebra with this property, we mean that if B' is anyother o-algebra with this property, then B' 2 B.)

Given that Ο denote the collection of all open subset of the real line ℝ. Claim: Borel sigma algebra…

Answered: Let O denote the collection of all open…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter6: More On Rings

Section6.1: Ideals And Quotient Rings

Problem 24E: 24. If is a commutative ring and is a fixed element of prove that the setis an ideal of . (The set...

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Let O denote the collection of all open subsets of the real line R. Prove that there is a smallest o-algebra B such that O C B. (By saying B is the smallest o-algebra with this property, we mean that if B' is any other o-algebra with this property, then B' 2 B.)