Project

The subject of our project was “Topological space and its properties”. To analyze this topic rigorously, we first described some elementary definitions and tried to interpret the core concepts of them by setting some regular, exceptional, and critical examples in the starting chapter. We added the definitions of some topological spaces, accumulation point, closure of a set, coarser and finer topology, relative topology, subspace, base, subbase, local base etc.

Next, we discussed various properties of a topological space, such as countability and separability. We also classified each of the properties and discussed every case in detail. Moreover, we have pointed out the so-called hereditary properties. 

Finally, we finished our discussion through a brief description about the application of topology. We identified the sectors where the concepts and knowledge of topology are applied successfully and gave real-life examples.