Let O be the collection of intervals Ia = (a,∞) where a ∈ R along with I∞ = ∅ andI−∞ = R. Does this collection define a topology? If so, prove that it does. Otherwise, justify why itdoes not. In case it does, describe A given A ⊂ R. Let O be the collection of intervals Ia=(a, ∞) where a € R along with I = 0 andI-∞ = R. Does this collection define a topology? If so, prove that it does. Otherwise, justify why itdoes not. In case it does, describe A given A CR.

Answered: Image /qna-images/answer/06478ef5-87bc-479b-9688-395527953b55.jpg

Let O be the collection of intervals Ia = (a, ∞) where a R along with I = 0 and I-∞ = R. Does this collection define a topology? If so, prove that it does. Otherwise, justify why it does not. In case it does, describe A given A CR.

Let O be the collection of intervals Ia = (a, ∞) where a R along with I = 0 and I-∞ = R. Does this collection define a topology? If so, prove that it does. Otherwise, justify why it does not. In case it does, describe A given A CR.

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter3: Functions

Section3.3: Rates Of Change And Behavior Of Graphs

Problem 2SE: If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local...

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Question

Let O be the collection of intervals Ia = (a,∞) where a ∈ R along with I∞ = ∅ and
I−∞ = R. Does this collection define a topology? If so, prove that it does. Otherwise, justify why it
does not. In case it does, describe A given A ⊂ R.