Continuous monotone decompositions of planar curves
Continuous multiplicative transformations
Continuous Relations.
Continuous selection theorems
Continuous approximation selection theorems are given. Hence, in some special cases continuous versions of Fillipov's selection theorem follow.
Continuous selections and approximations in α-convex metric spaces
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.
Continuous selections and countable sets
Continuous selections for a class of non-convex multivalued maps
Continuous selections for Lipschitz multifunctions.
Continuous selections, -subsets of Banach spaces and usco mappings
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.
Continuous Selections in α-Convex Metric Spaces
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.
Continuous selections of finite-set valued mappings
Continuous selections on spaces of continuous functions
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...
Continuous version of the Choquet integral representation theorem
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...
Contra--continuous and almost contra--continuous.
Contra-continuous functions and strongly -closed spaces.
Contractibility and a generalization of absolute extensor
Contracting the socle in rings of continuous functions
Contra-pre-semi-continuous functions.
Contra-semicontinuous functions.