Parametric Bing and Krasinkiewicz Maps: Revisited
نویسنده
چکیده
Let M be a complete metric ANR-space such that for any metric compactum K the function space C(K,M) contains a dense set of Bing (resp., Krasinkiewicz) maps. It is shown that M has the following property: If f : X → Y is a perfect surjection between metric spaces, then C(X,M) with the source limitation topology contains a dense Gδ-subset of maps g such that all restrictions g|f(y), y ∈ Y , are Bing (resp., Krasinkiewicz) maps. We apply the above result to establish some mapping theorems for extensional dimension.
منابع مشابه
Krasinkiewicz Spaces and Parametric Krasinkiewicz Maps
We say that a metrizable space M is a Krasinkiewicz space if any map from a metrizable compactum X into M can be approximated by Krasinkiewicz maps (a map g : X → M is Krasinkiewicz provided every continuum in X is either contained in a fiber of g or contains a component of a fiber of g). In this paper we establish the following property of Krasinkiewicz spaces: Let f : X → Y be a perfect map b...
متن کاملContinuity of the Solution Maps for Generalized Parametric Set-Valued Ky Fan Inequality Problems
Under new assumptions, we provide suffcient conditions for the upper and lower semicontinuity and continuity of the solution mappings to a class of generalized parametric set-valued Ky Fan inequality problems in linear metric space. These results extend and improve some known results in the literature e.g., Gong, 2008; Gong and Yoa, 2008; Chen and Gong, 2010; Li and Fang, 2010 . Some examples a...
متن کاملHölder continuity of solution maps to a parametric weak vector equilibrium problem
In this paper, by using a new concept of strong convexity, we obtain sufficient conditions for Holder continuity of the solution mapping for a parametric weak vector equilibrium problem in the case where the solution mapping is a general set-valued one. Without strong monotonicity assumptions, the Holder continuity for solution maps to parametric weak vector optimization problems is discussed.
متن کاملInfinite Order Parametric Normal Form of Hopf Singularity
In this paper, we introduce a suitable algebraic structure for efficient computation of the parametric normal form of Hopf singularity based on a notion of formal decompositions. Our parametric state and time spaces are respectively graded parametric Lie algebra and graded ring. As a consequence, the parametric state space is also a graded module. Parameter space is observed as an integral doma...
متن کاملCountable Connected Hausdorff and Urysohn Bunches of Arcs in the Plane
In this paper, we answer a question by Krasinkiewicz, Reńska and Sobolewski by constructing countable connected Hausdorff and Urysohn spaces as quotient spaces of bunches of arcs in the plane. We also consider a generalization of graphs by allowing vertices to be continua and replacing edges by not necessarily connected sets. We require only that two “vertices” be in the same quasi-component of...
متن کامل