EDB — 1PH

[1PH] We will use the definitions and results of the Section [2CF]↺↻, in particular [0YD]↺↻.

Fix \(\tilde𝛾:ℝ→ X\) continuous and periodic (of period \(1\)); we can define the map \(\hat𝛾:S^ 1→ X\) through the relation

Show that this is a good definition, and that \(\hat𝛾\) is continuous.

Use the exercise [0V8]↺↻ to show that every closed simple arc, when viewed equivalently as a map \(\hat𝛾:S^ 1→ X\), is a homeomorphism with its image.