# day 1

We will be covering the basic notions: topological spaces, compactness, homeomorphisms, homotopy,
and introduce the most important class of models for data analysis: manifolds.

Homework:

1. Three cyclists start and end in the same formation, A>B>C. During the race, they never are simultaneously at the same position. Also, we know that A took leadership from B 6 times, and B took leadership away from A 4 times and that C took leadership from B 3 times. How many times B took leadership away from C?
2. Describe glueing mapping $$\phi_N\circ \phi_S^{-1}$$ between two natural charts in two-dimensional sphere.