Does this form a topology?

  1. I am told that the interval (a, ∞) where a [itex]\in[/itex] (0, ∞) together the empty set and [0, ∞) form a topology on [0, ∞).

    But I thought in a topology that the intersection if any two sets had to also be in the topology, but the intersection of say (a, ∞) with (b, ∞) where a<b is surely (a,b) which isn't in the topology?

    Help! Thanks!
     
  2. jcsd
  3. Given any nonepty set X, the collection (empty set, X) is a topology. It is called "trivial topology". Please, check that it indeed satisfies all the axioms of a topological space.
     
  4. the intersection of (a,∞) and (b,∞) where a<b is (b,∞), not (a,b).
     
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