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October 5th, 2016, 01:46 PM   #1
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show that τ is not a topology

How do I solve this problem: Let τ be a set such asτ= {R, ∅} ∪ {Bq, q∈Q} where Bq=] q,+∞ [∩Q. Show that (R,τ) isn't a topological space.?
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October 5th, 2016, 02:13 PM   #2
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Originally Posted by Eria View Post
How do I solve this problem: Let τ be a set such asτ= {R, ∅} ∪ {Bq, q∈Q} where Bq=] q,+∞ [∩Q. Show that (R,τ) isn't a topological space.?
Clarify:
Quote:
asτ
Quote:
Bq=] q,+∞ [∩Q
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April 17th, 2017, 07:08 AM   #3
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HINT: Show that it contradicts or doesn't satisfy one of the axioms for a topology on a set.
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April 18th, 2017, 11:26 AM   #4
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Quote:
Clarify:
asτ
There is a missing space. It should have been "such as τ="
Quote:
Bq=] q,+∞ [∩Q
That pretty standard notation- the set of all real numbers larger than q intersect the set of all rational numbers- i.e.. the set of all rational numbers larger than q.
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