I study functional analysis. From time to time I find that the basics of many concepts lie on the concepts of topology.
I am familiar with basic concepts of topology. When I go deeper then wild things start.
I am not interested in topology for the sake of topology. I need it for a deep understanding of functional analysis.
Question 1: Is there any good book on topology for my purpose?
Question 2: If I really want to be good in functional analysis do I need study the whole topology or I can be satisfied by the standard topology?
Question 3: My question shows my lack of understanding and immaturity in mathematics. I should not be distracted from the main curriculum. Yes or no?
(My area of interest is harmonic analisys and operator theory. I am newbie).