20 Curve[1NT]

Let \((X,d)\) be a metric space.

We postpone the study of closed curves to the next section.

Here are two notions of equivalence of curves. The first was taken from an earlier version of the the lecture notes  [ 3 ] .

The second is Definition 7.5.4 from chapter 7 section 6 in the notes  [ 3 ] .

Exercises

1. [1J8]↺↻

2. [1NY]↺↻

3. [1P0]↺↻

4. [1P1]↺↻

5. [1P3]↺↻

6. [1P5]↺↻

7. [1P7]↺↻

20.1 Closed curves

We add other definitions to those already seen in [1NV]↺↻.

Exercises

1. [1PC]↺↻

2. [1PF]↺↻

3. [1PG]↺↻

4. [1PH]↺↻

In the following we will use periodic maps to represent the closed curves.

Exercises

1. [1PK]↺↻

2. [1PN]↺↻

3. [1PQ]↺↻

4. [1PR]↺↻

5. [1PT]↺↻

Other exercises regarding curves are [0ZG]↺↻, [17W]↺↻, [1H3]↺↻ and [1TJ]↺↻; see also Section [1QB]↺↻.