Locally Convex Topologies Induced by Fuzzy Norms

Abstract

It is shown that a Hausdorff topological vector space E is fuzzy normable iff its topology is a metrizable locally convex topology. Subspaces, product and quotient spaces of fuzzy normed spaces are investigated. Also the notion of the tensor product of two fuzzy normed norms is introduced and it is proved that the induced locally convex topology coincides with the projective tensor product topology.

The functional space in fuzzy analysis

“…2014 年, Nadaban 和 Dzitac [48] [49] 也证明了他的模糊 范数可诱出局部凸拓扑. 总之, 从不同角度出发, 有许多模糊范数概念被提出, 其研究范围相应地涉及 经典泛函分析方面颇广, 可以说模糊泛函分析的研究正在发展中.…”

Atomic Decompositions of Fuzzy Normed Linear Spaces for Wavelet Applications

“…Thus we can say that a clear definition regarding the fuzzy norm has not been reached, but after T. Bag and S.K. Samanta, almost all authors have had as a starting point their definition and, at the same time, they have tried to simplify and improve it: Saadati and Vaezpour, 2005;Miheţ, 2009;Goleţ, 2010;Alegre and Romaguera, 2010;Katsaras, 2013. The concept of fuzzy metric space was introduced by Kramosil and Michálek (1975) and many notions and results belonging to classical metric spaces could be extended and generalized in the context of fuzzy metric spaces. To some extent, the existence of an equivalence between the probabilistic metric spaces and fuzzy metric spaces, makes it to be impossible to speak about fuzzy normed linear spaces without making reference to the concept of probabilistic normed spaces introduced by A.N.…”