[News] - Video Lectures Algebraic Topology ( for Undergraduates )

Video lectures Algebraic Topology recorded at the university of Sydney, Australia.

Algebraic topology is the study of shapes. In the first lecture you will learn that a mathematician calls his donut a torus:

How to turn a sphere inside out.

Mind-blowing, fascinating, -must see- video. I think stuff like this is studied in Topology. The actual transformation what would it be like? Most likely complex analytic stuff. Hope to discover rather sooner than later.

Topology

Let X be any set and let T be a family of subsets of X. Then T is a topology on X if
- both the empty set and X are elements of T,
- any union of elements of T is an element of T, and
- any intersection of finitely many elements of T is an element of T.
If T is a topology on X, then X together with T is called a topological space.

Example:
X = {a,b,c} is a set.
T = {0, {a,b,c}, {a,b}, {a,c}, {b,c}. {a}, {b}, {c} } is a family of subsets.
[X, T] is a topological space.

From "Topology Without Tears" by

Sidney A. Morris.

At last an accessible topology book...

... from Dover Books ( who else?! ).



For 15,80 euro you get a truly beautiful (pocket)book.

After browsing the first pages I am now able to prove Euler's formula on Polyhedra, the beautiful F(aces) - E(dges) + V(ertices) = 2. I can even explain what a polyhedron is in these few, simple and (in fact) beautiful words: A polyhedron is a complex which is topologically equivalent to a sphere.