Neighborhood assignments and cardinal functions: a unified approach to metrization and uniformity

We use neighborhood assignments and cardinal functions to give a unified approach to metrizability and uniformity. This leads to a number of characterizations of m(X), the metrizability degree of X, u(X), the uniform weight of X, and w(X), the weight of X. For X normal (and regular), m(X) = u(X); it is unknown whether this result extends to completely regular spaces.