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Vector integral equations with discontinuous right-hand side

Filippo CammarotoPaolo Cubiotti — 1999

Commentationes Mathematicae Universitatis Carolinae

We deal with the integral equation u ( t ) = f ( I g ( t , z ) u ( z ) d z ) , with t I = [ 0 , 1 ] , f : 𝐑 n 𝐑 n and g : I × I [ 0 , + [ . We prove an existence theorem for solutions u L ( I , 𝐑 n ) where the function f is not assumed to be continuous, extending a result previously obtained for the case n = 1 .

Monotone weak Lindelöfness

Maddalena BonanzingaFilippo CammarotoBruno Pansera — 2011

Open Mathematics

The definition of monotone weak Lindelöfness is similar to monotone versions of other covering properties: X is monotonically weakly Lindelöf if there is an operator r that assigns to every open cover U a family of open sets r(U) so that (1) ∪r(U) is dense in X, (2) r(U) refines U, and (3) r(U) refines r(V) whenever U refines V. Some examples and counterexamples of monotonically weakly Lindelöf spaces are given and some basic properties such as the behavior with respect to products and subspaces...

On Relative γ k -Sets

Maddalena BonanzingaFilippo CammarotoBruno A. Pansera — 2007

Bollettino dell'Unione Matematica Italiana

In this note we show a relative version of γ k -set introduced and studied in [12]. We give several characterizations of this property; in particular one of the characterizations is Ramsey theoretical. Also we give a result involving a property of the corresponding mapping between function spaces.

H-closed functions

Filippo CammarotoVitaly V. FedorcukJack R. Porter — 1998

Commentationes Mathematicae Universitatis Carolinae

The notion of a Hausdorff function is generalized to the concept of H-closed function and the concept of an H-closed extension of a Hausdorff function is developed. Each Hausdorff function is shown to have an H-closed extension.

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