Continuous relations and generalized sets
Continuous approximation selection theorems are given. Hence, in some special cases continuous versions of Fillipov's selection theorem follow.
In the paper, the notion of a generalized convexity was defined and studied from the view-point of the selection and approximation theory of set-valued maps. We study the simultaneous existence of continuous relative selections and graph-approximations of lower semicontinuous and upper semicontinuous set-valued maps with α-convex values having nonempty intersection.
Every l.s.cṁapping from a paracompact space into the non-empty, closed, convex subsets of a (not necessarily convex) -subset of a Banach space admits a single-valued continuous selection provided every such mapping admits a convex-valued usco selection. This leads us to some new partial solutions of a problem raised by E. Michael.
The existence of continuous selections is proved for a class of lower semicontinuous multifunctions whose values are closed convex subsets of a complete metric space equipped with an appropriate notion of convexity. The approach is based on the notion of pseudo-barycenter of an ordered n-tuple of points.
For a space , we denote by , and the hyperspaces of non-empty closed, compact, and subsets of cardinality of , respectively, with their Vietoris topology. For spaces and , is the space of continuous functions from to with its pointwise convergence topology. We analyze in this article when , and have continuous selections for a space of the form , where is zero-dimensional and is a strongly zero-dimensional metrizable space. We prove that is weakly orderable if and...
Let E be a locally convex topological Hausdorff space, K a nonempty compact convex subset of E, μ a regular Borel probability measure on E and γ > 0. We say that the measure μ γ-represents a point x ∈ K if for any f ∈ E*. In this paper a continuous version of the Choquet theorem is proved, namely, if P is a continuous multivalued mapping from a metric space T into the space of nonempty, bounded convex subsets of a Banach space X, then there exists a weak* continuous family of regular Borel...
We demonstrate that the set of topologically distinct inverse limit spaces of tent maps with a Cantor set for its postcritical ω-limit set has cardinality of the continuum. The set of folding points (i.e. points at which the space is not homeomorphic to the product of a zero-dimensional set and an arc) of each of these spaces is also a Cantor set.
In this paper, we show that the C1 interior of the set of all continuum-wise expansive diffeomorphisms of a closed manifold coincides with the C1 interior of the set of all expansive diffeomorphisms. And the C1 interior of the set of all continuum-wise fully expansive diffeomorphisms on a surface is investigated. Furthermore, we have necessary and sufficient conditions for a diffeomorphism belonging to these open sets to be Anosov.
In this paper the concept of fuzzy contra -continuity in the sense of A. P. Sostak (1985) is introduced. Some interesting properties and characterizations are investigated. Also, some applications to fuzzy compact spaces are established.