Thread: Countability in topological spaces

Hi,

I need to prove the following:
Consider the topological space with the euclidian topology. Define an equivalence relation on as follows . Now, consider the quotient topology on then this space is neither (first countable axiom) nor (second countable axiom), because there doens't exist a countable base for the neighbourhoud filter of .

Can someone explain this for me?

Thanks!

How to prove,in topological space,every compact space is separable.?