1st Semester

Topology is the generalization of metric space. The word Topology is composed of two words: Top (means twisting instrument), Logy (a Latin word means Analysis). So Topology means twisting analysis. To describe the subject of topology is to say that it is qualitative geometry. The idea is that if one geometric object can be continuously transformed into another, then two objects are to be viewed as topologically the same. For example, a circle and a square are topologically equivalent. Physically, a rubber band can be stretched into the form of either a circle or a square. A figure eight curve formed by two circles touching at a point is to be regarded as topologically distinct from a circle or square. The term used to describe two geometric objects that are topologically equivalent is homeomorphic. Thus a circle and a square are homeomorphic.