Some characterization of c-paracompact and c-collectionwise normal spaces by continuous selections (II).
Some characterizations of c-paracompact and c-collectionwise normal spaces by continuous selections (I).
In this note we characterize the c-paracompact and c-collectionwise normal spaces in terms of continuous selections. We include the usual techniques with the required modifications by the cardinality.
Some refinements of a selection theorem with O-dimensional domain
The following known selection theorem is sharpened, primarily, by weakening the hypothesis that all the sets φ(x) are closed in Y: Let X be paracompact with dimX = 0, let Y be completely metrizable and let φ:X → 𝓕(Y) be l.s.c. Then φ has a selection.
Some representations of midconvex set-valued functions.
Some theorems on measurable and continuous selections and some applications
Strongly paracompact metrizable spaces
Strongly paracompact metrizable spaces are characterized in terms of special S-maps onto metrizable non-Archimedean spaces. A similar characterization of strongly metrizable spaces is obtained as well. The approach is based on a sieve-construction of "metric"-continuous pseudo-sections of lower semicontinuous mappings.
Subopen multifunctions and selections
Sur les sélecteurs des multifonctions
The generalization of Cellina's Fixed Point Theorem
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...
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 Selection Theorems
Uniformly continuous selections
Upper quasi continuous maps and quasi continuous selections
The paper deals with the existence of a quasi continuous selection of a multifunction for which upper inverse image of any open set with compact complement contains a set of the form , where is open and , are from a given ideal. The methods are based on the properties of a minimal multifunction which is generated by a cluster process with respect to a system of subsets of the form .
Wandering Sets for a Class of Borel Isomorphisms of ...0,1).
Weak orderability of second countable spaces
We demonstrate that a second countable space is weakly orderable if and only if it has a continuous weak selection. This provides a partial positive answer to a question of van Mill and Wattel.
Weak orderability of some spaces which admit a weak selection
We show that if a Hausdorff topological space satisfies one of the following properties: a) has a countable, discrete dense subset and is hereditarily collectionwise Hausdorff; b) has a discrete dense subset and admits a countable base; then the existence of a (continuous) weak selection on implies weak orderability. As a special case of either item a) or b), we obtain the result for every separable metrizable space with a discrete dense subset.
Weak selections and flows in networks
We demonstrate that every Vietoris continuous selection for the hyperspace of at most 3-point subsets implies the existence of a continuous selection for the hyperspace of at most 4-point subsets. However, in general, we do not know if such ``extensions'' are possible for hyperspaces of sets of other cardinalities. In particular, we do not know if the hyperspace of at most 3-point subsets has a continuous selection provided the hyperspace of at most 2-point subsets has a continuous selection.
Weak selections and weak orderability of function spaces
It is proved that for a zero-dimensional space , the function space has a Vietoris continuous selection for its hyperspace of at most 2-point sets if and only if is separable. This provides the complete affirmative solution to a question posed by Tamariz-Mascarúa. It is also obtained that for a strongly zero-dimensional metrizable space , the function space is weakly orderable if and only if its hyperspace of at most 2-point sets has a Vietoris continuous selection. This provides a partial...
Well posedness for evolution inclusions.