کد مقاله کد نشریه سال انتشار مقاله انگلیسی ترجمه فارسی نسخه تمام متن
4661570 1344843 2016 15 صفحه PDF ندارد دانلود رایگان
عنوان انگلیسی مقاله
Apartness spaces and uniform neighbourhood structures
ترجمه فارسی عنوان
فضاهای تفکیکی و ساختارهای محله ای یکنواخت
کلمات کلیدی
سازنده؛ رابطه تفکیکی ؛ ساختار محله یکنواخت؛ ساختار یکنواخت؛ کاملا محدود
03F60; 54E05; 54E15; 03F55Constructive; Apartness relation; Uniform neighbourhood structure; Uniform structure; Totally bounded
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات منطق ریاضی
چکیده انگلیسی

Two notions of ‘neighbourhood structure’ are compared within a constructive framework, before a third, new notion is introduced: that of a pre-uniform neighbourhood structure. It is shown that with every basic uniform neighbourhood structure on an inhabited set there is associated a natural set–set apartness relation. A large class of uniform neighbourhood spaces is produced by a construction that classically gives the unique totally bounded uniform structure inducing the given apartness on a symmetric T1 apartness space with the Efremovič property. Thus although, constructively, it remains unknown (and very unlikely) that such an apartness is generally induced by a uniform structure, it closely corresponds with a uniform neighbourhood structure. Uniform neighbourhood structures also provide a setting for notions of total boundedness and continuity akin to those in uniform spaces.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Annals of Pure and Applied Logic - Volume 167, Issue 9, September 2016, Pages 850–864
نویسندگان
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