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Darboux type properties of the paratingent

Małgorzata Fedor, Joanna Szyszkowska (2008)

Annales UMCS, Mathematica

In this paper we consider the Darboux type properties for the paratingent. We review some of the standard facts on the multivalued functions and the paratingent. We prove that the paratingent has always the Darboux property but the property D* holds only when the paratingent is a multivalued function.

Decomposable hulls of multifunctions

Andrzej Nowak, Celina Rom (2002)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

Let F be a multifunction with values in Lₚ(Ω, X). In this note, we study which regularity properties of F are preserved when we consider the decomposable hull of F.

Dense Continuity and Selections of Set-Valued Mappings

Kenderov, Petar, Moors, Warren, Revalski, Julian (1998)

Serdica Mathematical Journal

∗ The first and third author were partially supported by National Fund for Scientific Research at the Bulgarian Ministry of Science and Education under grant MM-701/97.A theorem proved by Fort in 1951 says that an upper or lower semi-continuous set-valued mapping from a Baire space A into non-empty compact subsets of a metric space is both lower and upper semi-continuous at the points of a dense Gδ -subset of A. In this paper we show that the conclusion of Fort’s theorem holds under the weaker...

Densely continuous forms, pointwise topology and cardinal functions

Dušan Holý, Peter Vadovič (2008)

Czechoslovak Mathematical Journal

We consider the space $D (X, Y)$ of densely continuous forms introduced by Hammer and McCoy and investigated also by Holá . We show some additional properties of $D (X, Y)$ and investigate the subspace $D^{*} (X)$ of locally bounded real-valued densely continuous forms equipped with the topology of pointwise convergence $τ_{p}$ . The largest part of the paper is devoted to the study of various cardinal functions for $(D^{*} (X), τ_{p})$ , in particular: character, pseudocharacter, weight, density, cellularity, diagonal degree, $π$ -weight, $π$ -character,...

Diametrically contractive multivalued mappings.

Dhompongsa, S., Yingtaweesittikul, H. (2007)

Fixed Point Theory and Applications [electronic only]

Differential inclusions in the Almgren sense on unbounded domains

Johnny Henderson, Abdelghani Ouahab (2014)

Annales Polonici Mathematici

We prove the existence of solutions of differential inclusions on a half-line. Our results are based on an approximation method combined with a diagonalization method.

Dugundji spaces and topological groups

Dmitriĭ B. Shakhmatov (1990)

Commentationes Mathematicae Universitatis Carolinae

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