topology

1. space

1.1. hausdorf

1.1.1. product topology

1.1.2. not: zariski with R

1.2. topology

1.2.1. definition

1.2.2. product topology

1.2.3. dis/connected

1.2.4. examples

1.2.5. homotopy equivalent

1.2.6. basis

1.3. connected

1.3.1. simply

1.4. path connected

1.4.1. product

1.5. metric

1.5.1. check

1.5.2. open

1.5.3. hausdorff?

1.6. contractible

1.6.1. iff any 2 continouus functions homotopic

2. subsets

2.1. open set

2.2. open ball

2.2.1. union

2.2.2. intersection

3. fundamental group

3.1. detailed definition

3.2. calculate using degree, eg for torus

3.3. winding number

4. degree

4.1. explain how used to compute pi1

4.2. calculate

4.3. angle function

5. map

5.1. homotopy

5.1.1. ~

5.1.2. homotopic functions

5.2. homeomorphism

5.2.1. interval to R

5.3. continuous map

5.3.1. composition

5.4. path