As we have been defined various concepts related to topological space and their subsets. Now we would like to discus the functions sending one topological space to another. The concepts of continuity of functions is one of the most important in topology. In this post, we shall formulate a definition of continuity and study their various properties.
The Continuous Function on Topological Space
Here you could learn about Topological Spaces and its interesting examples. Apart of this you will learn generation of topology from basis, new topological spaces from old, closed set, closure set, interior set etc.
Topological Spaces and their Examples
We can learn about matrix and some important operations om matrix with given lectures notes.
We are familiar with the notion of a basis for a finite dimensional vector space. It is a minimal collection of vectors that spans the vector space. If we know a basis, we can always recover the vector space. A basis for a topology is in a quite similar fashion a family of open subsets that `span’ the topology. If we know a basis, then we can find the topology for given set. There is no good notion of minimality for a basis here, so there is no such requirement, but it is often convenient to have a basis with as few elements as possible.
Download the lecture notes form following link.
2 Basis for Topology LN
In this lecture notes we are going to introduce the topological space which is primary object of study in field of topology. In first section, we give definition of topological space which is based on some axioms. In second section, we give interesting and interdisciplinary examples of topological spaces which help to understand basic theory of topology. You can download lecture note by clicking below.
1 Topological Space and their Examples