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.(adsbygoogle = window.adsbygoogle || []).push({});

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?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# A sequence or a single point?

**Physics Forums | Science Articles, Homework Help, Discussion**