An isomorphism of quantales is a

bijection from one quantale to another that preserves joins and meets of any cardinality and multiplication.

[P.sub.1]: [F.sup.f.sub.n] is a continuous function, positive and strictly increasing on the interval [mathematical expression not reproducible] and realizes a

bijection on the interval [mathematical expression not reproducible] that is to say, [F.sup.f.sub.n] must have the following: a limit 1 to the point [x.sub.imp]; that is to say, [mathematical expression not reproducible]; a limit 0 to the point [x.sub.ind]; that is to say, [mathematical expression not reproducible].

This order allows considering a

bijection yn from N"+1 to N, defined by

Otherwise, a collineation of the affine plane A is a

bijection of set P on yourself [14], that preserves lines.

As we have seen before, in order to define a partial action of a group G on a set X, we have to assign to each element g [member of] G a

bijection [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] between two subsets of X such that the compositions of these

bijections, wherever they are defined, should be compatible with the group operation.

The proof is based on Corteel and Nadeau's

bijection between permutation tableaux and permutations.

This construction produces a simple

bijection from [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] to the set [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] of permutations in [F.sub.n] having the succession set equal to [I.sub.[sigma]].

A

bijection : V E {1,...,| V | | E |} is an H -magic labeling of G if there exist a positive integer c (called the magic constant), such that for any subgraph H (V , E) of isomorphic to H , the sum (v) (e) is equal to magic constant c .

Since the pathweights are all distinct, the function w induces a

bijection between the paths of T and the elements of the group [Z.sub.k].

He showed that there exists an order-preserving

bijection between the set of cones in S and the set of left amenable partial orders on S.

It's easy to see that existence of [psi] requires [PSI] to be

bijection, we denote [psi] = [[PHI].sup.-1].

Then there is a

bijection between the set of subgroups of G/N and the set of subgroups of G which contain N such that: