In this essay, I describe two logics of space that are operative in responses to the COVID-19 pandemic. Quarantine partitioning is unavoidable and widespread. As a mode of governing, it presents a logic of space understood through its divisibility, making this logic seem like a given. Using the topological concept of a sphere eversion, I describe an alternative way of understanding spaces of quarantine as surroundings that we are exposed to or in contact with. I locate this alternative logic of space within already existing practices and concerns around public spaces newly invested with the possibility of exposure to and exposing others.