Geodesic
Nearness Convergence
Canadian mathematical bulletin, Tome 33 (1990) no. 3, pp. 268-272

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DOI

In this paper, a concept of nearness convergence is introduced which contains the proximal convergence of Leader as a special case. It is proved that uniform convergence and this nearness convergence are equivalent on totally bounded uniform nearness spaces. One of the features of this convergence is that it lies between uniform convergence and pointwise convergence, and implies uniform convergence on compacta. Some other weaker notions of nearness convergence which are sufficient to preserve nearness maps are also discussed.
DOI : 10.4153/CMB-1990-044-5
Mots-clés : 54D25, 54E17, Convergence, nearness, uniform, totally bounded, Uniform convergence, proximal convergence, Dini convergence, Arzelà convergence, Leader convergence, Uniform convergence on compacta 
Naimpally, S. A.; Tikoo, Mohan L. Nearness Convergence. Canadian mathematical bulletin, Tome 33 (1990) no. 3, pp. 268-272. doi: 10.4153/CMB-1990-044-5
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     year = {1990},
     volume = {33},
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     doi = {10.4153/CMB-1990-044-5},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1990-044-5/}
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