On Topologies Generated by Filters of Relations

Autor:	P. J. Moody, Ralph Kopperman, Hans-Peter A. Künzi, P. M. Gartside, P. J. Collins
Rok vydání:	1993
Předmět:	Transitive relation Range (mathematics) Pure mathematics History and Philosophy of Science Degree (graph theory) General Neuroscience Mathematics::General Topology Regular space Monotonic function Space (mathematics) Network topology General Biochemistry Genetics and Molecular Biology Mathematics
Zdroj:	Annals of the New York Academy of Sciences. 704:53-69
ISSN:	1749-6632 0077-8923
DOI:	10.1111/j.1749-6632.1993.tb52509.x
Popis:	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.
Databáze:	OpenAIRE
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