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On Topologies Generated by Filters of Relations a
Author(s) -
COLLINS P. J.,
GARTSIDE P. M.,
KOPPERMAN R. D.,
KüNZI H. P. A.,
MOODY P. J.
Publication year - 1993
Publication title -
annals of the new york academy of sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.712
H-Index - 248
eISSN - 1749-6632
pISSN - 0077-8923
DOI - 10.1111/j.1749-6632.1993.tb52509.x
Subject(s) - metrization theorem , mathematics , network topology , transitive relation , monotonic function , space (punctuation) , topology (electrical circuits) , structuring , range (aeronautics) , pure mathematics , combinatorics , mathematical analysis , computer science , separable space , finance , economics , operating system , materials science , composite material
. 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.