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.
- Teacher: Ali Ahmed