$ in the sheaf $ Omega $ for $ operatorname{mathbf{Top}}(I) $ (Chapter 4). We have $ U!sim_{i}V $ iff $ U $ and $ V $ have the same intersection with some $ i $ - neighbourhood. We interpret this to mean that the statement “ $ U!=!V $ “ or “ $ x!in!U $ iff $ x!in!V $ “ is locally true at $ i $