Set-valued semimartingales are introduced as an extension of the notion of single-valued semimartingales. For such multivalued processes their semimartingale selection properties are investigated.
We consider the hyperspace of nonempty closed subsets of completely metrizable space endowed with the Wijsman topologies . If is separable and , are two metrics generating the topology of , every countable set closed in has isolated points in . For , this implies a theorem of Costantini on topological completeness of . We show that for nonseparable the hyperspace may contain a closed copy of the rationals. This answers a question of Zsilinszky.
We introduced the notion of -boundedness of a filtered family of operators in the Musielak-Orlicz sequence space of multifunctions. This notion is used to get the convergence theorems for the families of -linear operators, -dist-sublinear operators and -dist-convex operators. Also, we prove that is complete.
The main purpose of this paper is to establish general conditions under which -spaces are compact-covering images of metric spaces by using the concept of -covers. We generalize a series of results on compact-covering open images and sequence-covering quotient images of metric spaces, and correct some mapping characterizations of -metrizable spaces by compact-covering -maps and -maps.
We provide a necessary and sufficient condition under which a generalized ordered topological product (GOTP) of two GO-spaces is monotonically Lindelöf.
We study retracts of coset spaces. We prove that in certain spaces the set of points that are contained in a component of dimension less than or equal to n, is a closed set. Using our techniques we are able to provide new examples of homogeneous spaces that are not coset spaces. We provide an example of a compact homogeneous space which is not a coset space. We further provide an example of a compact metrizable space which is a retract of a homogeneous compact space, but which is not a retract of...
We introduce the notion of a strongly Whyburn space, and show that a space is strongly Whyburn if and only if is Whyburn. We also show that if is Whyburn for any Whyburn space , then is discrete.