Can anybody suggest me a good book on Metric Spaces. Although I am not new to this subject, but want to polish my knowledge. I want a book which can clearly clear my basics. I want to start from the basics. Kindly suggest me. Thanks a lot.
I suggest Topology of Metric Spaces by s. Kumaresan.
In the preface:
The aim is to give a very streamlined development of a course in metric space topology emphasizing only the most useful concepts, concrete
spaces and geometric ideas. To encourage the geometric thinking, I have
chosen large number of examples which allow us to draw pictures and
develop our intuition and draw conclusions, generate ideas for proofs.
To this end, the book boasts of a lot of pictures. A secondary aim is
to treat this as a preparatory ground for a general topology course and
arm the reader with a repertory of examples.
I suggest “Introductory Functional Analysis With Applications” By “Erwin Kreyszig”. Its 1st Chapter gives a very nice introduction to Metric Spaces… Good Luck