An Illustrated Introduction to Topological Spaces

Topology is an indispensable object of study with open sets as well as closed sets being the most fundamental concepts in topological space. Since then a lot of work has been done using these notions and many interesting results have been obtained. Several mathematicians have generalized these concepts.Quotient mapping starts among the important and most researched points in the whole Mathematical Science. Quotient mapping as being stronger than continuous mapping. Many different forms of maps ranging from continuous maps to irresolute and to quotient maps have been introduced over the years. Various interesting problems are encountered when one considers the study of these maps. Its importance is significant in various areas of Mathematics and related Science. The aim of this work is to introduce and study the interesting properties of quotient map.In topology and related branches of mathematics, a connected space is a topological space that cannot be represented as the union oftwo or more disjoint non-empty open subsets. Connectedness is one of the principal topological properties that are used to distinguish topological spaces.