In this paper, the notion of
a completely adequate neighborhood system for a topological space is defined and
used to obtain characterizations of discreteness and second countability.
Certain conditions on the completely adequate neighborhood system are given
which yield collection wise normality and paracompactness. The notion of
a standardized topological space is introduced (the class of standardized
spaces includes, among others, the separable spaces and the developable
spaces) and the main theorem gives necessary and sufficient conditions for the
metrizability of standardized spaces in terms of completely adequate neighborhood
systems.
