What continuity really is (pretentious heading to attract readership)

This is an article I wanted to write for a long time. What exactly is topological continuity? A mapping between two topological spaces is said to be continuous if for any open set , is open in . After reading this definition, very few students understand the motivation behind this definition. By bringing these concepts

Valuations, Absolute Values and Ostrowski’s theorem

This is a guest post by Abhishek Gupta. We know that there is an absolute value on the set of real numbers which assigns to any real number the non negative real number , its multiplicative and satisfies the triangle inequality. In this post we will abstract the notion absolute value for an arbitrary field and