A STRONG COMPLETENESS CONDITION IN UNIFORM SPACES WITH WELL ORDERED BASES
A natural strengthening of the completeness hypothesis, called -completeness, allows us to extend to ! -metric spaces some properties of complete metric spaces which fail to hold if only the completeness condi- tion is assumed. In this way we achieve some results on hyperspace theory, dealing with supercompleteness and with selections of multivalued functions. The notion of -completeness is investigated and it is proved that quite important classes of ! -metric spaces have this property.
The Dugundji extension property can fail in $ω_μ$ -metrizable spaces
We show that there exist ωμ-metrizable spaces which do not have the Dugundji extension property (21 with the countable box topology is such a space). This answers a question posed by the second author in 1972, and shows that certain results of van Douwen and Borges are false.
Conserved Quantities of a Class of Nonlinear Difference-Difference Equations
Higher-order conserved quantities of a class of nonlinear difference-difference equations which are related to the discrete-time Toda equation are obtained using the Miura transformations.