Order Topology

• Find the \(4^{th}\) Lecture cum Tutorial notes linked: MA 406 Lecture Notes (1-4), (Google Drive Link)
• Given a set \(X\) with a linear (simple) order, we can construct a topology called the order topology on \(X\). This is based on the intervals that can be defined thanks to the linear structure imposed by the simple order.
• In \(\mathbb{R}\), the order topology coincides with the standard topology, however in \(\mathbb{R}^2\), the order topology (induced from dictionary order) is different from the standard topology.