Connectedness 1 (Topology)

We start with the simplest definition of connectedness of a topological space. WE show that our definition is equivalent to the one found in books. We then investigate the connectedness or otherwise of the examples in our list of spaces. We also observe that R with the usual topology is connected. I thank Vinod, Ishwarya and Aman Bharoadia for the timestamps. 0:00 Introduction 0:45 Brief description about this series 3:17 Intuitive Ideas of connectedness 5:50 Definition- Connectedness 11:09 Connectedness about R 12:00 Definition- Separation of X 18:09 Review 19:10 Example: Discrete topology 21:30 Example: Indiscrete topology 22:20 Fact: Any two nonempty open sets in X intersect implies X is connected 24:30 Application of the last fact to cofinite and co-countable Topology. 29:55 Example: VIP Topology 31:03 Example: Outcast Topology 33:18 Example: Lower limit Topology 34:25 Example: R2 with using Dictionary Order Topology 36:35 Definition of a connected subset 38:18 Example: R\{0} of R with usual topology is not connected.