Convergence questions are treated by considering vector spaces "V" carrying a compatible topology, a structure that allows one to talk about elements being close to each other. Compatible here means that addition and scalar multiplication have to be continuous maps. Roughly, if x and y in "V", and "a" in "F" vary by a bounded amount, then so do and . To make sense of specifying the amount a scalar changes, the field "F" also has to carry a topology in this context; a common choice are the reals or the complex numbers.