A manifold is “a set in which we understand how different numbers in the set are connected to each other…”
Spacetime is a manifold of events and it is endowed with a metric.
A metric is some kind of mathematical object that gives us a notion of distance.
Appendix A
“A manifold is a continuous space of points.”
We love this and changed it to the following:
A manifold is a set of points that creates a continuous space.