2019/02/21 by Tristan Bice, Bice, Tristan
Mathematics · Medicine · #06A06 #06A07 #54D10 #54D30 #54D35 #54D45 #54D70 #54D80 #54E15 #54E17 #54E35 #54E45 #54E50 #54H10 #Category Theory (math.CT) #Cell Adhesion Molecules Research #FOS: Mathematics #General Topology (math.GN) #Homotopy and Cohomology in Algebraic Topology #Systemic Lupus Erythematosus Research #math.CT #math.GN #msc:06A06 #msc:06A07 #msc:54D10 #msc:54D30 #msc:54D35 #msc:54D45 #msc:54D70 #msc:54D80 #msc:54E15 #msc:54E17 #msc:54E35 #msc:54E45 #msc:54E50 #msc:54H10
paper · pdf · doi:10.48550/arxiv.1902.07948
arxiv created 2019/02/21 · openalex publication_date 2019/02/21 · arxiv updated 2019/02/22 · openalex created_date 2024/04/10 · openalex updated_date 2026/07/28
We extend nearness frames to posets representing bases and even subbases of T1 spaces. This allows us to put a classic duality due to Wallman, between compact T1 spaces and abstract simplicial complexes, into a general nearness framework. Within this framework we extend Wallman's duality to locally compact T1 spaces and, with further modifications, to completely metrisable spaces. Moreover, we provide an elementary sublocale-free version of an admissibility condition due to Picado and Pultr and show how it strengthens Wallman's admissibility condition.