On a lemma of Mathematics

R. G. Meades and U. Clidd
(Received by the Editor 1.4.1996)

The aim of this paper, which fills a much-needed gap in the literature, is to generalize the abstractions of the extensions in [1] to special cases of particular incidences of concrete examples in [2], thereby producing several solutions to which there are no known problems. The main theorem is trivial, so is omitted, but the proof is given for completeness.

Consider the following non-associative diagram shown above.

Since the necessity and sufficiency of the statement is obvious, we prove only the reverse implication. By constructing the canonical category and applying the usual decomposition theorem it is then easy to see, using a result implicit in [3] and an unpublished series of lemmas by the third author, that the standard representation functive is hemi-biregular, pseudo-strongly normal, upper completely simple, semi-countably fundamental and sub-extremally superintegral, but only regular, normal, simple, fundamental and integral.

The same proof, with a completely different theorem, appears in [4].

To sum up, therefore, note that the result is proved.

To end with, I should point out that the method is so completely general that no special applications are possible.

In conclusion, we would like to thank the referee for the proof of Theorem 3.

Finally, the author wants most sincerely to be able to acknowledge a Research Grant.


  1. Rosenkrantz, A and Guildenstern, F.-J. A survey of the general theory of surveys. Zap. Zurn. Uc. Ped. Gos. Inst. Mat. Fiz. Nauk Uzb. S.S.R. (3rd series) 22(19)17A-B(3/4)(1972), vol.31(1971-73), 3141-2718. (Uzbek. Georgian summary.)
  2. Beane, J., Gorne, K. and Dunnett, L. Fibres in bundles of sheaves. Farmer's Weekly (to appear).