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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We strengthen a theorem of Gitik and Shelah [6] by showing that if κ is either weakly inaccessible or the successor of a singular cardinal and S is a stationary subset of κ such that NSκ S is saturated then κ \S is fat. Using this theorem we derive some results about the existence of fat stationary sets. We then strengthen some results due to Baumgartner and Taylor [2], showing in particular th...
متن کاملNon - separable Banach spaces with non - meager Hamel basis
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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Let (X, d, T ) be a dynamical system, where (X, d) is a compact metric space and T : X → X a continuous map. We introduce two conditions for the set of orbits, called respectively g-almost product property and uniform separation property. The g-almost product property holds for dynamical systems with the specification property, but also for many others. For example all β-shifts have the g-almos...
متن کاملHamel bases and well–ordering the continuum
In ZF, the existence of a Hamel basis does not yield a well–ordering of R. Throughout this paper, by a Hamel basis we always mean a basis for R, construed as a vector space over Q. We denote by E the Vitali equivalence relation, xEy iff x− y ∈ Q for x, y ∈ R. We also write [x]E = {y : yEx} for the E–equivalence class of x. A transversal for the set of all E–equivalence classes picks exactly one...
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ژورنال
عنوان ژورنال: Tatra Mountains Mathematical Publications
سال: 2015
ISSN: 1210-3195
DOI: 10.1515/tmmp-2015-0011