Measure theoretic zero sets in infinite dimensional spaces and differentiability of Lipschitz mappings
Measure-Theoretic Characterizations of Certain Topological Properties
It is shown that Čech completeness, ultracompleteness and local compactness can be defined by demanding that certain equivalences hold between certain classes of Baire measures or by demanding that certain classes of Baire measures have non-empty support. This shows that these three topological properties are measurable, similarly to the classical examples of compact spaces, pseudo-compact spaces and realcompact spaces.
Metric characterizations of Banach spaces
Metric enrichment, finite generation, and the path coreflection
We prove a number of results involving categories enriched over CMet, the category of complete metric spaces with possibly infinite distances. The category CPMet of path complete metric spaces is locally -presentable, closed monoidal, and coreflective in CMet. We also prove that the category CCMet of convex complete metric spaces is not closed monoidal and characterize the isometry--generated objects in CMet, CPMet and CCMet, answering questions by Di Liberti and Rosický. Other results include...
Minimizing convex functions by continuous descent methods.
Mittag-Leffler methods in analysis.
In this survey we present two Mittag-Leffler lemmas and several applications to topics as varied as the delta-equation, Fréchet algebras, inductive limits of Banach spaces and quasi-normable Fréchet spaces.
Multi-valued contraction mappings in complete metric spaces
Multivalued generalized contractions and fixed point theorems