منابع مشابه
Measure and Other Properties of a Hamel Basis
A Hamel basis is a set a, ô, c, • • • of real numbers such that if x is any real number whatsoever then x may be expressed uniquely in the form aa+(3b+yc + • • • where a, j8, 7, • • • are rational numbers of which only a finite number are different from zero. Since each of these sums is formed from a finite number of nonzero terms and the coefficients a, /3, 7, • • • are rational and therefore ...
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A different approach is given to recent results due mainly to R.C. Johnson and A. Leal Duarte on the multiplicities of eigenvalues of a Hermitian matrix whose graph is a tree. The technics developed are based on some results of matchings polynomials and use a work by O.L. Heilmann and E.H. Lieb on an apparently unrelated topic.
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We show that an infinite-dimensional complete linear space X has: • a dense hereditarily Baire Hamel basis if |X| ≤ c; • a dense non-meager Hamel basis if |X| = κ = 2 for some cardinal κ. According to Corollary 3.4 of [BDHMP] each infinite-dimensional separable Banach space X has a non-meager Hamel basis. This is a special case of Theorem3.3 of [BDHMP], asserting that an infinite-dimensional Ba...
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In this paper we give a characterization for all semigroups whose square is a group. Moreover, we axiomatize such semigroups and study some relations between the class of these semigroups and Grouplikes,introduced by the author. Also, we observe that this paper characterizes and axiomatizes a class of Homogroups (semigroups containing an ideal subgroup). Finally, several equivalent conditions ...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2002
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-02-06620-0