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.

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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.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.2: Mappings

Problem 19E

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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.

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.

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