The homotopies of admissible multivalued mappings
Certain properties of homotopies of admissible multivalued mappings shall be presented, along with their applications as the tool for examining the acyclicity of a space.
The intersection convolution of relations and the Hahn-Banach type theorems
By introducing the intersection convolution of relations, we prove a natural generalization of an extension theorem of B. Rodrí guez-Salinas and L. Bou on linear selections which is already a substantial generalization of the classical Hahn-Banach theorems. In particular, we give a simple neccesary and sufficient condition in terms of the intersection convolution of a homogeneous relation and its partial linear selections in order that every partial linear selection of this relation can have an...
The Lefschetz fixed point theorem for multivalued maps of non-metrizable spaces
The Lefschetz fixed point theorem for some noncompact multi-valued maps
The Lindelöf number greater than continuum is u-invariant
2000 Mathematics Subject Classification: 54C35, 54D20, 54C60.Two Tychonoff spaces X and Y are said to be l-equivalent (u-equivalent) if Cp(X) and Cp(Y) are linearly (uniformly) homeomorphic. N. V. Velichko proved that countable Lindelöf number is preserved by the relation of l-equivalence. A. Bouziad strengthened this result and proved that any Lindelöf number is preserved by the relation of l-equivalence. In this paper it has been proved that the Lindelöf number greater than continuum is preserved...
The multicores in metric spaces and their application in fixed point theory
This paper discusses the notion, the properties and the application of multicores, i.e. some compact sets contained in metric spaces.
Theorems on multifunctions satisfying a rational inequality
Tightness of compact spaces is preserved by the -equivalence relation
We prove that if there is an open mapping from a subspace of onto , then is a countable union of images of closed subspaces of finite powers of under finite-valued upper semicontinuous mappings. This allows, in particular, to prove that if and are -equivalent compact spaces, then and have the same tightness, and that, assuming , if and are -equivalent compact spaces and is sequential, then is sequential.
Topological and approximation methods of degree theory of set-valued maps [Book]
Topological degrees of set-valued compact fields in locally convex spaces [Book]
Topological essentiality for multivalued weighted mappings
Topological structure of solution sets: current results
Topologies, continuity and bisimulations
Topologies, Continuity and Bisimulations
The notion of a bisimulation relation is of basic importance in many areas of computation theory and logic. Of late, it has come to take a particular significance in work on the formal analysis and verification of hybrid control systems, where system properties are expressible by formulas of the modal μ-calculus or weaker temporal logics. Our purpose here is to give an analysis of the concept of bisimulation, starting with the observation that the zig-zag conditions are suggestive of some...
Topologies On Spaces Of Continuous Multifunctions
Transfer positive hemicontinuity and zeros, coincidences, and fixed points of maps in topological vector spaces.
Trivial bundles of spaces of probability measures and countable-dimensionality
The probability measure functor P carries open continuous mappings of compact metric spaces into Q-bundles provided Y is countable-dimensional and all fibers are infinite. This answers a question raised by V. Fedorchuk.
Two theorems on the Scorza Dragoni property for multifunctions
We point out two theorems on the Scorza Dragoni property for multifunctions. As an application, in particular, we improve a Carathéodory selection theorem by A. Cellina [4], by removing a compactness assumption.
Uniform convergence on spaces of multifunctions
Uniqueness and non uniqueness of optimal maps in mass transport problem with not strictly convex cost
In the setting of the optimal transportation problem we provide some conditions which ensure the existence and the uniqueness of the optimal map in the case of cost functions satisfying mild regularity hypothesis and no convexity or concavity assumptions.