Various surfaces | Section 1 |

A cube with holes | |

Trefoil knot | Section 1 |

Folding a square to make a torus | |

The torus as a quotient of the plane | |

Letters of the alphabet | Section 1 |

Letters grouped by type | Section 1 |

Cage with two or three holes | Section 1 |

Simplices | Section 1 |

Barycentric coordinates | |

Different triangulations of the sphere | Section 1 |

The triangle and the square | Section 1 |

Skeleta of simplices | Section 1 |

Open sets | Definition 3.8 |

Finite element model | Remark 2.3 |

A cylinder is homeomorphic to an annulus | Example 4.7 |

Stereographic projection | Example 4.10 |

$\mathbb{R}P^1$ is homeomorphic to $S^1$ | Example 8.23 |

Gluing two discs to make a sphere | Example 8.24 |

Loops on the sphere | |

Loops on the torus | |

A homotopy of the trefoil | |

Geometry of the Möbius strip | Example 10.23 |

The Möbius strip and the circle | Example 10.23 |

The punctured plane | Example 10.23 |

The punctured sphere | |

The punctured torus | Remark 15.26 |

Wrapping an annulus | Example 15.27 |

The exponential map | |

The exponential map is a covering | Proposition 12.6 |

Path lifting | Proposition 12.9 |

Homotopy lifting | Proposition 12.12 |

Boundary of a tetrahedron | Example 18.7 |

Barycentric subdivision of a tetrahedron | Example 22.5 |

The map $\mu\colon|K'|\to|K|$ | Example 22.8 |