|کد مقاله||کد نشریه||سال انتشار||مقاله انگلیسی||ترجمه فارسی||نسخه تمام متن|
|4661570||1344843||2016||15 صفحه PDF||ندارد||دانلود کنید|
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.
Journal: Annals of Pure and Applied Logic - Volume 167, Issue 9, September 2016, Pages 850–864