Poston, T. (1971) Fuzzy geometry. PhD thesis, University of Warwick.
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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 or Dissertation (PhD)|
|Subjects:||Q Science > QA Mathematics|
|Library of Congress Subject Headings (LCSH):||Fuzzy topology|
|Institution:||University of Warwick|
|Theses Department:||Mathematics Institute|
|Supervisor(s)/Advisor:||Brown, R. ; Rees, Elmer G. ; Cockcroft, W. H. (Wilfred Halliday) ; Zeeman, E. C. (Erik Christopher), 1925-|
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