Dear, I'm ALessandro Rosa. While translating an article from French, I met this terminology "ensemble d'un seul tenant", but, even if I understood what it means, I cannot find out a proper analogue expression in english. Could you help me, please ? Thanks. Alessandro Rosa.

  Question N°1 of Alessandro Rosa the 15/09/01 at 10h 16 :

Please asnwer to my question included in the title
of this e-mail : Correct translation in english of Feuillet.
Answer to malilla2000@yahoo.it

Thanks.
Alessandro Rosa

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A set is defined "consisting of one piece" [d'un seul tenant] between two of its points if, given a value e > 0, one can find out a sequence (of points in the set) starting and ending in two given points, so that the distance from each point to the following point is smaller than e. Effectively, even if it has not been stated in the usual canonical form, we can agree on the term "compact". Don't we ? Thank for support. Alessandro Rosa

  Answer of Jean Jacquelin for the question N°2 the  15/12/01 at 19h 38 :

"Ensemble d'un seul tenant" :

This terminology is not perfectly clear for me without knowing the context of use. Possibly, it might mean "Compact Set".

" A Set S is compact if, from any sequence of elements X1, X2, ... of S, a subsequence can always be extracted which tends to some limit element X of S. Compact sets are therefore closed and bounded "  [ E.W.Weisstein,  CRC Concise Encyclopedia of Mathematics, Chapman & Hall, p.282, 1999].

According to this definition, check if the translation is correct in the context of use. I suspect that "Compact Set" might be more restrictive than "Ensemble d'un seul tenant". A clear definition of this expression should be necessary in order to achive an exact translation.

  Answer of Jean Jacquelin for the question N°1 the  20/09/01 at 14h 51 :

On my opinion, the best translation in english of "feuillet" might be "Leaf". For example, the word "Leaf" is defined in CRC Concise Encyclopedy of Mathematics, E.W.Weisstein, Chapman & All, p.1044, 1999 : LEAF (FOLIATION) : Let M_n be an n-Manifold and let F={F_a} denote a Partition of M into disjoint path-connected subsets. Then if F is a FOLIATION of M, each F_a is called a LEAF and is not necessarily closed or compact.

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