Time: 16:10-17:00

venue: Mathematics Building Room 312

Speaker: Dr. Wei-Ming Wang  (Center for General Education, National Formosa University)

Title: A Review on Non-Archimedean Analysis: An Introduction to Ultrametric Spaces

Abstract:

The difference between usual metric spaces and ultrametric spaces is the “level” of triangle inequality. Ultrametric spaces possess a stronger version of triangle inequality. With this behavior, there are much different results than usual metric spaces in Classical Analysis. This gives birth to the area so-called Non-Archimedean Analysis.

In this talk, we give a simple approach to Non-Archimedean Analysis including:

• An introduction to ultrametric spaces;

• The strong triangle inequality and some related amazing results that can’t occur in Classical Analysis;

• The relation between strong triangle inequality and Archimedean property.

KEYWORDS: Archimedean property, strong triangle inequality, ultrametric, ultrametric space.