Manifolds #2 - Topological Manifolds

Notes are on my GitHub! github.com/rorg314/WHYBmaths In this video I formalise the concept of a (topological) manifold. We will see that a manifold is a topological space which we have 'covered' in charts. A chart is an open subset of the manifold along with a chart map which maps the chart into R^d. These charts can be interpreted as giving a way to talk about the points of an abstract topological space using concrete coordinates. I briefly allude to the notion of changing coordinates using a transition function (discussed in more detail in the next video).