کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
6424559 | 1344250 | 2015 | 17 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Topological representation of lattice homomorphisms
ترجمه فارسی عنوان
نمایندگی توموگرافی هومومورفیسم های شبکه
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کلمات کلیدی
شبکه توزیعی، فاکتور والمن، دوگانگی سنگ، جبر بولی،
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
هندسه و توپولوژی
چکیده انگلیسی
Wallman [13] proved that if L is a distributive lattice with 0 and 1, then there is a T1-space with a base (for closed subsets) being a homomorphic image of L. We show that this theorem can be extended over homomorphisms. More precisely: if NLat denotes the category of normal and distributive lattices with 0 and 1 and homomorphisms, and Comp denotes the category of compact Hausdorff spaces and continuous mappings, then there exists a contravariant functor Ult:NLatâComp. When restricted to the subcategory of Boolean lattices this functor coincides with a well-known Stone functor which realizes the Stone Duality. The functor W carries monomorphisms into surjections. However, it does not carry epimorphisms into injections. The last property makes a difference with the Stone functor. Some applications to topological constructions are given as well.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Topology and its Applications - Volume 196, Part B, December 2015, Pages 362-378
Journal: Topology and its Applications - Volume 196, Part B, December 2015, Pages 362-378
نویسندگان
Wojciech Bielas, Aleksander BÅaszczyk,