\(\newcommand{\from}{\colon}\)\(\newcommand{\cross}{\times}\)Questions handed in by a student on 2017-10-11. Lecture - 1. [Two paragraphs about the problem of proving that \(T_3\), the three-regular tree, is contractible, ending with a question as to whether or not a certain construction is well-defined.] Ans: Your question has so many "moving parts" that I'd prefer to discuss it in person, say in office hours. In particular, some of the notation you introduce requires more explanation. 2. How can I visualise the homotopic relation? Ans: Suppose that \(f, g \from X \to Y\) are homotopic maps. Thus there is a homotopy \(F \from X \cross I \to Y\) giving a one-parameter family \( \{f_t\} \) of maps that start at \(f_0 = f\) and end at \(f_1 = g\). One way to visualise all of this is by imagining the images \(f_t(X)\) moving through \(Y\). Another way is to draw a picture of \(X \cross I\) (for example, as a square) and label parts of \( X \cross I \) by where they are sent by \(F\).