Hutton, Bruce (1976) Fuzzy topological spaces. PhD thesis, University of Warwick.

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Abstract

(1) We define normality for fuzzy topological spaces, define a fuzzy unit interval, and prove a Urysohn type lemma.

(2) We define uniformities on fuzzy lattices, and characterise uniformizability in terms of complete regularity.

(3) We define the product of a collection of fuzzy topological spaces. We define compactness and connectedness, and show that the product is compact (connected) iff each factor space is.

(4) We place normality and complete regularity within a coherent hierarchy of separation and regularity axioms. We prove the usual implications, and the usual theorems about compactness and products.

(5) We give alternative definitions of uniformities and pseudometrics, and show a compact R1 space has a unique uniformity.

Item Type:	Thesis or Dissertation (PhD)
Subjects:	Q Science > QA Mathematics
Library of Congress Subject Headings (LCSH):	Fuzzy topology
Official Date:	1976
Dates:	Date Event 1976 Submitted
Institution:	University of Warwick
Theses Department:	Mathematics Institute
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Elworthy, K. D.
Extent:	108, [2] leaves
Language:	eng

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