More details on metric spaces and the Euclidean space are available in standard real analysis textbooks, for example (Rudin, 1976). A more general presentation of open sets and continuity that does not assume the presence of a metric space is available in topology textbooks, for example (Munkres, 2000). Much of the material presented in Section B.4 holds also for infinite dimensional vector spaces. More details are available in standard functional analysis textbooks, for example (Kolmogorov, 1999).