Poston, T. (1971) Fuzzy geometry. PhD thesis, University of Warwick.

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Abstract

The concept of fuzzy space is due independently to
Poincaré and Zeeman. (Poincaré
used the term "physical continuum", Zeeman the term
"tolerance space". I have reluctantly introduced a
third expression since my attempts to generate a
vocabulary from either of these have all proved
impossibly unwieldy.) Both were led to it by the
nature of our perception of space, and both adapted to
it tools current in topology. Unfortunately, neither
examined the application of these tools in complete
detail, and as a result the argument from analogy
was somewhat over-extended by both. The resemblances
to topology are strong; the differences are sometimes
glaring and sometimes subtle. In the latter case the
difficulties produced by a topologically-conditioned
intuition can be severe obstacles to progress.
(Certainly, having been reared mathematically as a
topologist I have found it necessary to distrust any
conclusion whose proof is not painfully precise. )
For this reason many of the proofs in this paper are
set out in somewhat more detail than would be natural
in a more established field. For this reason also I
have here not only set out the positive results I
have so far obtained in the subject but, for the
benefit of topologists, elaborated on the failures of
analogy with topology where a more succinct exposition
would have ignored them as dead ends (e.g., in Chap. I, §2).

Item Type:	Thesis (PhD)
Subjects:	Q Science > QA Mathematics
Library of Congress Subject Headings (LCSH):	Fuzzy topology
Official Date:	June 1971
Dates:	Date Event June 1971 Submitted
Institution:	University of Warwick
Theses Department:	Mathematics Institute
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Brown, R. ; Rees, Elmer G. ; Cockcroft, W. H. (Wilfred Halliday) ; Zeeman, E. C. (Erik Christopher), 1925-
Extent:	177 p.
Language:	eng

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