کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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4661570 | 1633438 | 2016 | 15 صفحه PDF | دانلود رایگان |
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