topology; Banach–Tarski paradox
torus is product of \(S^1 X S^1\) can also model torus as fiber bundle mobius strip can be modelled as finite length on a circle, which is twisted. NB base space is a circle going through the strip, not a length of one of the intersection things.
Fiber bundle Vs higher dimensional manifold Local symmetry possible Model functions on manifold
fibre bundle \(E->B\) where E is an element in the total space, and B is an element in the base space.
Topology: open cover and sub cover. Open cover is a collection of open sets which collectively include all points in S. Sub cover is subset of open xover which still covers S. Related to compactness