metric: characterize the open sets of a subspace (i.e. the subspace topology)
metric: state the sequential characterization of functional limits
Reboot the blov.
metric: fix the definition of connectedness to stipulate that the partitioning sets are nonempty.
add notes on real analysis
metric: state that composition of continuous functions is continuous
metric: Move sequences up in the document, before compactness. Begin proving compactness iff sequential compactness.