14 research outputs found
Fuzzy uniformities on function spaces
[EN] We study several uniformities on a function space and show that the fuzzy topology associated with the fuzzy uniformity of uniform convergence is jointly fuzzy continuous on Cf (X, Y ) ,the collection of all fuzzy continuous functions from a fuzzy topological space X into a fuzzy uniform space Y . We define fuzzy uniformity of uniform convergence on starplus-compacta and show that its corresponding fuzzy topology is the starplus-compact open fuzzy topology. Moreover, we introduce the notion of fuzzy equicontinuity and fuzzy uniform equicontinuity on fuzzy subsets of a function space and study their properties.Kohli, J.; Prasannan, A. (2006). Fuzzy uniformities on function spaces. Applied General Topology. 7(2):177-189. doi:10.4995/agt.2006.1922.SWORD1771897
The Kolmogorov-Riesz compactness theorem
We show that the Arzela-Ascoli theorem and Kolmogorov compactness theorem
both are consequences of a simple lemma on compactness in metric spaces. Their
relation to Helly's theorem is discussed. The paper contains a detailed
discussion on the historical background of the Kolmogorov compactness theorem.Comment: This version is lightly revised in response to referee comments. The
paper will appear in Expositiones Mathematica