 In a first-countable space (such as a metric space), it is enough to consider only convergent sequences, instead of all nets.One value of this characterization is that it may be used as a definition in the context of convergence spaces, which are more general than topological spaces.Notice that this characterization also depends on the surrounding space "X", because whether or not a sequence or net converges in "X" depends on what points are present in "X".