Resumen de Approach Vector Spaces

Stijn Verwulgen, Robert Lowen

• In this paper we determine what properties an approach structure has to fulfil for it to concord well with a vector space structure. Not surprisingly these conditions are more subtle than those for a topology. That the conditions we impose are the right ones follows mainly from the good categorical relationship among the different categories which play an important role in this setting, namely topological vector spaces, completely regular spaces, metrizable vector spaces and of course approach vector spaces.