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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.)

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.)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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See below picture: 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 0-algebra with this property, we mean that if B' is any other o-algebra with this property, then B' 2 B.)
Transcribed Image Text:See below picture: 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 0-algebra with this property, we mean that if B' is any other o-algebra with this property, then B' 2 B.)
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