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There are several well defined abstract spaces contrast the familiar Euclidean space, namely Metric spaces, Normed spaces, Function spaces, Hilbert spaces and Banach spaces,  etc. To give a overview of these abstract spaces and potential connections between these spaces. This post is dedicated to that purpose. The post is based on Terrence Tao‘s article ‘Function Spaces’ , Timothy Gowers‘s ‘Normed space and banach spaces’ and ‘Metric spaces’, which are published in Princeton Companion to the Mathematics (PCM). About PCM, I have a short post for it or even much better link for further information. Read the rest of this entry »


This is fabulas book. The editor-in-Chief is  Timothy Gowers who need no introduction and June Barrow-Green is an assistant editor (with particular expertise in the history of mathematics). The central focus of the book will be to describe modern pure mathematics, in all its diversity, in a way that is serious, sometimes quite detailed, but always accessible at the lowest possible level. It is very helpful for person like me in particular, who love math and finding ways to study math seriously, as the book take each topic very seriously, trying to be understandable even to the beginner (fundamental definitions are explained clearly with follow up examples) and explanations are given in considerably detail. 


There is a website dedicated to it. To promote this great publication, I have no mean to keep its website secret– PCM. Furthermore, You can get into this site with userid Guest and password PCM (at least it works for this moment, I hope it will be forever).