ISSN:
1420-8903
Keywords:
Primary 39B40
;
Secondary 22A05, 06F05
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Summary Consideration of the Associativity Equation,x ∘ (y ∘ z) = (x ∘ y) ∘ z, in the case where∘:I × I → I (I a real interval) is continuous and satisfies a cancellation property on both sides, provides a complete characterization of real continuous cancellation semigroups, namely that they are topologically order-isomorphic to addition on some real interval: ( − ∞,b), ( − ∞,b], −∞, +∞), (a, + ∞), or [a, + ∞) — whereb = 0 or −1 anda = 0 or 1. The original proof, however, involves some awkward handling of cases and has defied streamlining for some time. A new proof is given following a simpler approach, devised by Páles and fine-tuned by Craigen.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01836453
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