Topología Elemental

A course on Elements of Topology (TOEL, see detailed contents), 3rd year in the Maths Degree and Double Degrees (with Computer Sciences and with Physics). The part of the course devoted to the fundamental group follows a 2019 text written jointly with J.D. Porras and M. Jaenada, fully revised in this second edition; the relevant sections are 1-9, 11-12, 16, 19, 30, 31. Samples of problems and exercises are these 234 and for exam models look here. Sierpinski’s is a quite general theorem, illustrating the beauty of General Set Topology, kindly written by Manuel Morán. Here there is a bonus on the fundamental group of a surface. In the end, enjoy these two 3blue1brown’s videos: Unsolved and Fair Division, brought to my atention by David Pérez.

Estos son esquemas aproximados de las lecciones que se imparten durante el curso: L1, L2, L3, L4, L5, L6, L7, L8, L9, L10, L11, L12, L13, L14, L15, L16, L17, L18, L19, L20, L21, L22, L23, L24, L25, L26, L27, L28.

Tres animaciones para L26: cross-cup, suma de dos torosbotella de Klein.
Otra para L27: un proyectivo más un toro es igual a un proyectivo más una botella de Klein.