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

TOPOLOGIES IN FUZZY LOCALLY CONVEX SPACES

Our purpose is to give an overview of weak topologies in a fuzzy locally convex space. Firstly, we introduce locally convex spaces in fuzzy context. Furthermore fuzzy version of a semi - norm is obtained. Finally, we introduce a weak topology on a fuzzy locally convex space and the weak star topology on its dual as a generalization of usual weak topology. A special attention is also given to some properties of X- topology on X*, called fuzzy weak star topology

A construction of a fuzzy topology from a strong fuzzy metric

[EN] After the inception of the concept of a fuzzy metric by I. Kramosil and J. Michalek, and especially after its revision by A. George and G. Veeramani, the attention of many researches was attracted to the topology induced by a fuzzy metric. In most of the works devoted to this subject the resulting topology is an ordinary, that is a crisp one. Recently some researchers showed interest in the fuzzy-type topologies induced by fuzzy metrics. In particular, in the paper  (J.J. Mi\~{n}ana, A. \v{S}ostak, {\it Fuzzifying topology induced by a strong fuzzy metric}, Fuzzy Sets and Systems,  6938 DOI information: 10.1016/j.fss.2015.11.005.) a fuzzifying topology ${\mathcal T}:2^X \to [0,1]$ induced by a fuzzy metric  $m: X\times X \times [0,\infty)$ was constructed. In this paper we extend  this construction to get the fuzzy topology ${\mathcal T}: [0,1]^X \to [0,1]$ and study some properties of this fuzzy topology.54AGrecova, S.; Sostak, A.; Uljane, I. (2016). 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