L Space In ZFC

1. The document discusses S-spaces and L-spaces, which are types of topological spaces that are hereditarily separable or hereditarily Lindelöf. 2. It presents theorems showing the existence or nonexistence of S-spaces and L-spaces under different set theory assumptions, such as the existence of Suslin lines or adding Cohen reals. 3. The canonical form theorem states that S-spaces and L-spaces (when they exist) can be represented as subspaces of 2^ω1, the Tychonoff product of ω1 many 2-point discrete spaces.