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- Compactness of products. Tychonoff theorem (formulation). Baire category theorem (now for compact spaces).
- Homotopy of maps, homotopy equivalence of spaces, retraction and deformation retraction. Contractible spaces, examples. Homotopy path, loops.
- Fundamental group, homotopy invariance, the role of the base point. Fundamental group of the circle. Non-contractibility of the circle. Brouwer fixed point theorem for the 2-disk.