Abstract

It was shown [8] that uniform boundedness in a Serstnev PN space $(V,nu,tau,tau^*)$, (named boundedness in the present setting) of a subset $Asubset V$ 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. Section 2 presents a characterization of those PN spaces, whether they are TV spaces or not, in which the equivalence holds. In Section 3, a characterization of the Archimedeanity of triangle functions $tau^*$ of the type $tau_{T,L}$ is given. This work is a partial solution to a problem of comparing the concepts of distributional boundedness ($D$--bounded in short) and that of boundedness in the sense of associated strong topology.

Autore Pugliese

• Sempi Carlo

Tutti gli autori

• B. Lafuerza Guillén , C. Sempi , G. Zhang , M. Zhang

Titolo volume/Rivista

NONLINEAR ANALYSIS

Anno di pubblicazione

2010

ISSN

1751-570X

ISBN

Non Disponibile

Numero di citazioni Wos

Nessuna citazione

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Numero di citazioni Scopus

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Settori ERC

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Codici ASJC

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