Abstract
ABSTRACT. A range of topologies, generated in a “preuniform” manner, is shown to give conditions for a space to be (1) Nagata over a regular infinite cardinal α, and (2) α‐metrizable. Connections with the structuring mechanism introduced by P. J. Collins and A. W. Roscoe are investigated. The metrizability degree of a regular space is shown to be equal to the minimum among cardinals arising as weights of compatible local uniformities, and the reader is asked to characterize topologies admitting monotonic quasi uniformities. Various relevant cardinal invariants are discussed; in particular, comparisons are made involving the transitivity and γ‐degrees.
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