METRIC SPACE

This project work will introduced the reader to the concept of metrics (a class of functions which is regarded as generalization of the notion of distance) and metric spaces with examples. It emphasises the notion of vector space which generalizes
the concept of addition and scalar multiplication. The notion of inner product allows us to generalize the notion of the dot product of vectors. It also allows us to talk about angle between vectors, and their norms. We can discuss the notion of distance between vectors. Also the combination of inner product with a vector gives a scalar. An inner product space is a special type of vector space that has mechanism for computing a version of dot product that can be defined in real or complex vector space, as long as it satisfies some conditions. The properties arising from a metric in an inner product space is important example of a metric space