Universally Meager Sets
نویسنده
چکیده
We study category counterparts of the notion of a universal measure zero set of reals. We say that a set A ⊆ R is universally meager if every Borel isomorphic image of A is meager in R. We give various equivalent definitions emphasizing analogies with the universally null sets of reals. In particular, two problems emerging from an earlier work of Grzegorek are
منابع مشابه
Remarks on Small Sets of Reals
We show that the Dual Borel Conjecture implies that d > א1 and find some topological characterizations of perfectly meager and universally meager sets.
متن کاملUniversal Measure Zero, Large Hausdorff Dimension, and Nearly Lipschitz Maps
We prove that each analytic set in R contains a universally null set of the same Hausdorff dimension and that each metric space contains a universally null set of Hausdorff dimension no less than the topological dimension of the space. Similar results also hold for universally meager sets. An essential part of the construction involves an analysis of Lipschitzlike mappings of separable metric s...
متن کاملUncountable γ - sets under axiom CPA gamecube
In the paper we formulate a Covering Property Axiom CPA cube , which holds in the iterated perfect set model, and show that it implies the existence of uncountable strong γ-sets in R (which are strongly meager) as well as uncountable γ-sets in R which are not strongly meager. These sets must be of cardinality ω1 < c, since every γ-set is universally null, while CPA cube implies that every unive...
متن کاملOn Perfectly Meager Sets
We show that it is consistent that the product of perfectly meager sets is perfectly meager.
متن کاملLp Computable Functions and Fourier Series
This paper studies how well computable functions can be approximated by their Fourier series. To this end, we equip the space of L-computable functions (computable Lebesgue integrable functions) with a size notion, by introducing L-computable Baire categories. We show that L-computable Baire categories satisfy the following three basic properties. Singleton sets {f} (where f is L-computable) ar...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2000