This sheet is based on Lectures 1 and 2.

• Problem 1 is a minor variation of Lemma 2.2.
• Problems 2 and 3 may look scary, but they are really simple, you just need to unravel the definitions.
• Problems 4 shows that contractible spaces are the simplest objects in $\mathsf{hTop}$.
• Problem 5 is about the cone over a space. Bonus question: Show that the operation $X \to CX$ defines a functor on $\mathsf{Top}$ (you have to come up with what the functor does on morphisms!)

This problem sheet should hopefully be quite easy for most of you—they will get harder as the semester progresses! 😈

🤓 Feel free to ask a question if you are stuck! 🤓