I intend to start learning some topology on my own. I wonder How much metric spaces I should know in order to motivate the concepts of topology?
I know it's possible to learn topology without any knowledge of metric spaces. But I heard that knowing metric spaces will be good to motivate things.
Also , What resources do you recommend to gain this amount of knowledge of metric spaces ? I intend to learn metric spaces in the same time going through topology. Is that possible ? or the metric space needed is too much to be covered in the same time ?
I hope that your answers contain resources ( books , chapter of books , free notes on web , videos etc ... ) to learn this amount of metric spaces.
Note: I talk about point-set topology.