Symmetric linear functionals on the Banach space generated by pseudometrics
S. I. Nykorovych,
T. V. Vasylyshyn
Abstract:In this work we consider the notion of $B$-equivalence of pseudometrics.Two pseudometrics $d_1$ and $d_2$ on a set $X$ are called $B$-equivalent, where $B$ is a subgroup of the group of all bijections on $X,$ if there exists an element $b$ of $B$ such that $d_1(x,y) = d_2(b(x),b(y))$ for every $x,y\in X,$ that is, $d_1$ can be obtained from $d_2$ by permutating elements of $X$ with the aid of the bijection $b.$The group $B$ generates the group $\widehat B$ of transformations of the set of all pseudometricson $… Show more
Set email alert for when this publication receives citations?
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.