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    A study of boundedness in probabilistic normed spaces

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    Boundedness in PN spaces .pdf (4.144Mb)
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    URI: http://hdl.handle.net/10835/2751
    ISSN: 0362-546X/$; doi: 10.1016/j.na.2009.12.037
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    Author/s
    Lafuerza Guillén, Bernardo; Sempi, Carlo; Zhang, Gaoxun
    Date
    2010
    Abstract
    It was shown in Lafuerza-Guillén, Rodríguez- Lallena and Sempi (1999) that uniform boundedness in a Serstnev PN space (V,\un, \tau,\tau^*), (named boundeness in the present setting) of a subset A in V with respect to the strong topology is equivalent to the fact that the probabilistic radius R_A of A is an element of D^+. Here we extend the equivalence just mentioned to a larger class of PN spaces, namely those PN spaces that are topological vector spaces(briefly TV spaces), but are not Serstnev PN spaces. We present a characterization of those PN spaces, whether they are TV spaces or not, in which the equivalence holds. Then a charaterization of the Archimedeanity of triangle functions \tau^* of type \tau_{T,L} is given.This work is a partial solution to a problema of comparing the concepts of distributional boundedness (D-bounded in short) and that of boundedness in the sense of associated strong topology.
    Palabra/s clave
    Mathematics
    Probabilistic Normed Spaces
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    • Artículos de revista Dpto. Matemáticas [118]

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