
#1
Feb2712, 10:48 AM

P: 32

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
Feb2712, 11:13 AM

P: 1,412

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.




#3
Feb2712, 11:18 AM

P: 320




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