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 conceptsContinue reading “What continuity really is (pretentious heading to attract readership)”

Valuations, Absolute Values and Ostrowski’s theorem

ThisĀ 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 andContinue reading “Valuations, Absolute Values and Ostrowski’s theorem”