Hierarchy from Inner Product Spaces to Topological Spaces
TopologicalSpaces MetricSpaces FunctionalAnalysis
02:00 Abide by Reason reviews the hierarchy of spaces for students who know vectors and dot products but have not yet seen how these structures generalize to pure topology.
Definition of a Topological Space via Open Sets
TopologicalSpaces OpenSets SetTheory
06:00 Abide by Reason formalizes the notion of a topological space for learners who have seen neighborhoods and open intervals on (\mathbb{R}) but not the abstract definition.
Discrete, Indiscrete, and Intermediate Topologies on Finite Sets
TopologicalSpaces DiscreteTopology IndiscreteTopology
10:00 Abide by Reason illustrates concrete examples of topologies for students who benefit from finite, combinatorial pictures before thinking about infinite spaces.
Topology as Minimal Structure for Convergence and Continuity
TopologicalSpaces Convergence Continuity
14:00 Abide by Reason explains why topological spaces matter for viewers wondering what is gained by stripping away metrics and norms.