2015/04/10 by James F. Peters, J. F. Peters, Peters, J. F. +2 · 1 citation
Computer Science · Decision Sciences · Mathematics · #Advanced Algebra and Logic #Advanced Topology and Set Theory #Fuzzy and Soft Set Theory #math.GN #msc:54B20 #msc:54C08 #msc:54D05 #msc:54E05
paper · pdf · doi:10.48550/arxiv.1504.02740
11 pages, 10 figures
arxiv created 2015/04/10 · arxiv updated 2015/04/13
This article introduces strongly proximal continuous (s.p.c.) functions, strong proximal equivalence (s.p.e.) and strong connectedness. A main result is that if topological spaces X,Y are endowed with compatible strong proximities and f:X\longrightarrow Y is a bijective s.p.e., then its extension on the hyperspaces \CL(X) and \CL(Y), endowed with the related strongly hit and miss hypertopologies, is a homeomorphism. For a topological space endowed with a strongly near proximity, strongly proximal connectedness implies connectedness but not conversely. Conditions required for strongly proximal connectedness are given. Applications of s.p.c. and strongly proximal connectedness are given in terms of strongly proximal descriptive proximity.