ITES2001 - Fourth Italian-Spanish Conference on
GENERAL TOPOLOGY AND ITS APPLICATIONS
Bressanone, 27-30 June 2001

Hypertopologies and quasi-metrics
Jesús Rodríguez-López, Salvador Romaguera
Universidad Politécnica de Valencia, Spain

The abstract of the talk (see below) may be downloaded in one of the following formats:


We study the relation between the Wijsman topology of a
quasi-pseudo-metric space and others like the Vietoris, proximal
and Hausdorff quasi-uniform topology, respectively. In particular,
we prove that:
\begin{quote}\it
if $(X,\mathcal{T})$ is a quasi-pseudo-metrizable
topological space then its Vietoris topology is the supremum of
all Wijsman topologies generated by all quasi-pseudo-metrics
compatible with $\mathcal{T}.$
\end{quote}
Furthermore, we show that
\begin{quote}\it
the Wijsman topology of a quasi-pseudo-metric space $(X,d)$ coincides
with the Hausdorff
quasi-uniform topology if and only if the conjugate quasi-pseudo-metric $%
d^{-1}$ is hereditarily precompact.
\end{quote}


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