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
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:NLat→Comp. 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
نویسندگان
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