2015/03/09 by J. F. Peters, Peters, J. F., C. Guadagni +1
Mathematics · #FOS: Mathematics #General Topology (math.GN) #Primary 54E05 (Proximity) #Secondary 54B20 (Hyperspaces) #math.GN #msc:54B20 #msc:54E05
paper · pdf · doi:10.48550/arxiv.1503.02587
8 pages, 4 figures. arXiv admin note: text overlap with arXiv:1502.05913
arxiv created 2015/03/09 · arxiv updated 2015/03/10
This article introduces the \it strongly hit and far-miss as well as hit and strongly far miss hypertopologies on \textrmCL(X) associated with \mathscrB, a nonempty family of subsets on the topological space X. They result from the strong farness and strong nearness proximities. The main results in this paper stem from the Hausdorffness of (\textrmCL(X), τ_\doublevee, \mathscrB) and (\textrmRCL(X), τ^\doublewedge_\mathscrB ) , where \textrmRCL(X) is the space of regular closed subsets of X. To obtain the results, special local families are introduced.