Functional analysis and topology books needed

[discoversci]

Hi folks ... I urgently need good books about Functional analysis and Topology. These must be comprehensive and thorough, undergraduate or graduate. Please, advise and provide your experiences with such books. I accept only thick books ;)

e.g

• Introductory Functional Analysis with Applications by Erwin Kreyszig ?
• What about An introduction to functional analysis by Mischa Cotlar ?
• Topology by Munkres ?
• Introduction to Differential and Algebraic Topology by bunch of Russian guys ?

Many thanks in advance to all who reply !

 

[WannabeNewton]

Willard - General Topology

 

[jmjlt88]

The topology text by Munkres is absolutely amazing; it is also VERY comprehensive with respect to general topology. Depending on your background, you may also want to purchase Mendelson's Introduction to Topology (which is very cheap to purchase). The latter discusses metric spaces in much more depth than the Munkres text. I found that particularly useful because I never had an analysis course that touched upon the topic in anything more than a cursory way.

General Topology by Willard is also an excellent choice; however, in my opinion, it is a little bit tougher to read than the two aforementioned texts. His use of "nhood" in place of "neighborhood" also annoys me. :)