کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4657852 1633078 2016 22 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Products of derived structures on topological spaces
ترجمه فارسی عنوان
محصولات ساختارهای مشتق شده در فضاهای توپولوژی
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات هندسه و توپولوژی
چکیده انگلیسی

We consider topological spaces X   equipped with an algebra AA of subsets of X   and an ideal II of AA. Motivated by the example of the Jordan measurable subsets of RR, we consider the derived structure   obtained by replacing AA by the algebra ∂A={E∈A:∂E∈I}∂A={E∈A:∂E∈I} of sets with negligible boundaries, and II by ∂I=I∩∂A∂I=I∩∂A. In a previous paper by M.R. Burke et al. (2012) [7], the authors classified these derived structures (under some assumptions) and computed densities for them. In the present paper, we extend that work in the context of products of derived structures. We study in greater detail the box cross product γ⊠δγ⊠δ of two set maps γ∈P(X)Aγ∈P(X)A, δ∈P(Y)Bδ∈P(Y)B introduced in joint work of the authors with K. Musiał (2009) [6], examining when it preserves densities and other types of liftings. For preservation of monotonicity, we introduce a variation on the localization property of ideals which is well-known for the meager ideal. An examination of skew products provides a class of structures to which our results apply.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Topology and its Applications - Volume 201, 15 March 2016, Pages 247–268
نویسندگان
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