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Suppose we define a set A to consist of all sequences x=<x_i> of real numbers, for which some condition holds, define a metric on it, and show that it generates a topology T on A.

What i am a little unclear about is when we try to show if (A,T) is Hausdorff or not, do we pick now two points(single real numbers) x,y from A, and show that there are(are not) neighgorhoods U,V or x and y respectively that are disjoint, or do we pick sequences x and y of real numbers, instead?

My intuition says they should be sequences, but not quite sure about it.

Thanks for your help?

What i am a little unclear about is when we try to show if (A,T) is Hausdorff or not, do we pick now two points(single real numbers) x,y from A, and show that there are(are not) neighgorhoods U,V or x and y respectively that are disjoint, or do we pick sequences x and y of real numbers, instead?

My intuition says they should be sequences, but not quite sure about it.

Thanks for your help?

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