Decomposable hulls of multifunctions
Let F be a multifunction with values in Lₚ(Ω, X). In this note, we study which regularity properties of F are preserved when we consider the decomposable hull of F.
Decomposable inverse limits with a single bonding map on [0,1] below the identity
Decomposing Borel functions using the Shore-Slaman join theorem
Jayne and Rogers proved that every function from an analytic space into a separable metrizable space is decomposable into countably many continuous functions with closed domains if and only if the preimage of each set under that function is again . Many researchers conjectured that the Jayne-Rogers theorem can be generalized to all finite levels of Borel functions. In this paper, by using the Shore-Slaman join theorem on the Turing degrees, we show the following variant of the Jayne-Rogers theorem...
Decomposition in the product of a measure space and a Polish space
Decomposition of metric space into nowhere dense sets: A correction
Decomposition of metric spaces into nowhere dense sets
Decomposition of openness.
Decomposition of topologies on lattices and hyperspaces [Book]
Decomposition spaces and shape in the sense of Fox
Decomposition spaces having arbitrarily small neighborhoods with 2-sphere boundaries II
Decompositions into submanifolds of fixed codimension
Decompositions of cyclic elements of locally connected continua
Let X denote a locally connected continuum such that cyclic elements have metrizable boundary in X. We study the cyclic elements of X by demonstrating that each such continuum gives rise to an upper semicontinuous decomposition G of X into continua such that X/G is the continuous image of an arc and the cyclic elements of X correspond to the cyclic elements of X/G that are Peano continua.
Decompositions of which satisfy a uniform Lipschitz condition are factors of
Decompositions of manifolds into codimension one submanifolds
Decompositions of the state space, homomorphisms and products of semigroup acts
Decreasing (G) spaces
We consider the class of decreasing (G) spaces introduced by Collins and Roscoe and address the question as to whether it coincides with the class of decreasing (A) spaces. We provide a partial solution to this problem (the answer is yes for homogeneous spaces). We also express decreasing (G) as a monotone normality type condition and explore the preservation of decreasing (G) type properties under closed maps. The corresponding results for decreasing (A) spaces are unknown.
Dedekind cuts in C(X)
The aim of this paper is to show that every Hausdorff continuous interval-valued function on a completely regular topological space X corresponds to a Dedekind cut in C(X) and conversely.
Dedekind-Endlichkeit und Wohlordenbarkeit.
Definable completeness
Definably complete Baire structures
We consider definably complete Baire expansions of ordered fields: every definable subset of the domain of the structure has a supremum and the domain cannot be written as the union of a definable increasing family of nowhere dense sets. Every expansion of the real field is definably complete and Baire, and so is every o-minimal expansion of a field. Moreover, unlike the o-minimal case, the structures considered form an axiomatizable class. In this context we prove a version of the Kuratowski-Ulam...