countably many


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countably many

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x] = {v [member of] V: v(x) [member of] Z} is a periodic arrangement of countably many shifts of the hyperplane [H.
1] with finite length and a system of fibres as the union of at most countably many fibres that can have only the endpoints in common (see Stoyan et al.
alpha]]) just possibly for countably many indices [alpha] [member of] [0, [OMEGA][.
Then X is automatically pairwise Lindelof in this topology, since every open set only omits countably many points of X.
As long as it is produced recursively--like any other human language-it will only have countably many expressions (words, sentences, texts).
In this paper we prove that the eigenvalues of the underlying rational eigenproblem can be characterized as minmax values of a Rayleigh functional, from which we immediately obtain the existence of countably many real and positive eigenvalues.
In order to treat all symmetric functions at once, one passes to the case of countably many non-commuting variables [{[[upsilon].
n]-rectifiable if there exist countably many Lipschitz maps [g.
It is clear, that only for countably many g we have L([psi] [intersection]g) [not equal to] [empty set].
Example 5 Consider the Hopf algebra QSym of quasisymmetric functions in countably many variables, and the Hopf subalgebra Sym of symmetric functions.
Second, we propose to derive identities between partitions by looking at suitable ideals in a polynomial ring in countably many variables endowed with a natural grading.
A](a) must be irrational since there are uncountably many possible A but only countably many rational functions in Z((P)).