Recent content by beep300

Thanks everyone, I get the first and second countability axioms better now. I guess one shoud always look at how definitions from general topology apply to intuitive topological spaces (such as the metric space) to get a better grasp. Could one state this property, in other words: that given...

Thanks, I get it a lot better now. There's one thing I don't get though: What's the distinction between first-countable and second-countable spaces? What's the intuition behind them?

I need some help understanding the countability and separation axioms in general topology, and how they give rise to first-countable and second-countable spaces, T1 spaces, Hausdorff spaces, etc. I more or less get the formal definition, but I can't quite grasp the intuition behind them. Any...