کد مقاله کد نشریه سال انتشار مقاله انگلیسی ترجمه فارسی نسخه تمام متن
4661551 1344842 2017 18 صفحه PDF ندارد دانلود رایگان
عنوان انگلیسی مقاله
Products of Menger spaces: A combinatorial approach
ترجمه فارسی عنوان
محصولات فضاهای منگر: یک رویکرد ترکیبی
کلمات کلیدی
اولیه، ؛ ثانویه، اموال منگر؛ اموال Hurewicz؛ مجموعه کنسانتره؛ مجموعه دوجهته بیکران؛ ترازو
primary, 54D20; secondary, 03E17Menger property; Hurewicz property; Concentrated sets; Bi-unbounded sets; Reaping number; Scales
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات منطق ریاضی
چکیده انگلیسی

We construct Menger subsets of the real line whose product is not Menger in the plane. In contrast to earlier constructions, our approach is purely combinatorial. The set theoretic hypothesis used in our construction is far milder than earlier ones, and holds in almost all canonical models of set theory of the real line. On the other hand, we establish productive properties for versions of Menger's property parameterized by filters and semifilters. In particular, the Continuum Hypothesis implies that every productively Menger set of real numbers is productively Hurewicz, and each ultrafilter version of Menger's property is strictly between Menger's and Hurewicz's classic properties. We include a number of open problems emerging from this study.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Annals of Pure and Applied Logic - Volume 168, Issue 1, January 2017, Pages 1–18
نویسندگان
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