• 主题
高级搜索  >
历史搜索 清空历史
首页> 外文期刊>Real analysis exchange >MAGIC SETS
【24h】

MAGIC SETS

机译：魔术套装

获取原文
获取原文并翻译 | 示例
           
页面导航
  • 摘要
  • 著录项
  • 相似文献
  • 相关主题

摘要

In this paper we study magic sets for certain families H ⊆ ~ℝℝ which are subsets M ⊆ ℝ such that for all functions f,g ∈ H we have that g[M] ⊆ f[M] ⇒ f =g. Specifically we are interested in magic sets for the family G of all continuous functions that are not constant on any open subset of ℝ. We will show that these magic sets are stable in the following sense: Adding and removing a countable set does not destroy the property of being a magic set. Moreover, if the union of less than c meager sets is still meager, we can also add and remove sets of cardinality less than c without destroying the magic set.Then we will enlarge the family G to a family F by replacing the continuity with symmetry and assuming that the functions are locally bounded. A function f: ℝ→ℝ is symmetric iff for every x ∈ ℝ we have that lim_(h↓0) 1/2(f(x+h)+ f(x-h)) = f(x). For this family of functions we will construct 2~C pairwise different magic sets which cannot be destroyed by adding and removing a set of cardinality less than c. We will see that under the continuum hypothesis magic sets and these more stable magic sets for the family F are the same. We shall also see that the assumption of local boundedness cannot be omitted. Finally, we will prove that for the existence of a magic set for the family F it is sufficient to assume that the union of less than c meager sets is still meager. So for example Martin's axiom for δ-centered partial orders implies the existence of a magic set.
机译：在本文中，我们研究了某些族H⊆〜ℝℝ的魔术集，它们是M⊆的子集，因此对于所有函数f，g∈H，我们具有g [M]⊆f [M]⇒f = g。特别地，我们对所有连续函数族G的魔术集感兴趣，这些魔术函数在open的任何开放子集上都不恒定。我们将在以下意义上证明这些魔术集是稳定的：添加和删除可数集不会破坏成为魔术集的属性。此外，如果少于c个微集合的并集仍然很微不足道，我们还可以在不破坏魔术集的情况下添加和删除小于c个基数的集合，然后将对称性替换为连续性，从而将族G扩大到族F并假设函数是局部有界的。对于每个x∈f函数f：ℝ→ℝ是对称iff，我们有lim_（h↓0）1/2（f（x + h）+ f（x-h））= f（x）。对于这个函数系列，我们将构造2〜C个成对的不同魔术集，这些魔术集不能通过添加和除去小于c的基数来破坏。我们将看到，在连续假设下，魔术集和家庭F的这些更稳定的魔术集是相同的。我们还将看到，不能忽略局部有界的假设。最后，我们将证明对于家庭F而言，存在魔术集就足以假设少于c个微不足道集合的并集仍然是微不足道的。因此，例如，以δ为中心的偏序的马丁公理暗示了魔术集的存在。

著录项

相似文献

  • 外文文献
  • 中文文献
  • 专利
获取原文

客服邮箱：kefu@zhangqiaokeyan.com

京公网安备：11010802029741号 ICP备案号：京ICP备15016152号-6 六维联合信息科技 (北京) 有限公司©版权所有

  • 客服微信

  • 服务号