منابع مشابه
Extending Generalized Whitney Maps
For metrizable continua, there exists the well-known notion of a Whitney map. If X is a nonempty, compact, and metric space, then any Whitney map for any closed subset of 2X can be extended to a Whitney map for 2X [3, 16.10 Theorem]. The main purpose of this paper is to prove some generalizations of this theorem.
متن کاملMonotone Functions and Maps
In [1] we defined semi-monotone sets, as open bounded sets, definable in an o-minimal structure over the reals (e.g., real semialgebraic or subanalytic sets), and having connected intersections with all translated coordinate cones in Rn. In this paper we develop this theory further by defining monotone functions and maps, and studying their fundamental geometric properties. We prove several equ...
متن کاملWhitney Maps - a Non - Metric Case
It is shown that there is no Whitney map on the hyperspace 2x for nonmetrizable Hausdorff compact spaces X. Examples are presented of non-metrizable continua X which admit and ones which do not admit a Whitney map for C(X). Given a Hausdorff compact space X, we consider the space 2x of all non-empty compact subsets of X equipped with the Vietoris topology. Any subspace H (X) of the space 2x is ...
متن کاملMonotone Maps: a review
The aim of this paper is to provide a brief review of the main results in the theory of discrete-time monotone dynamics.
متن کاملGeneralized Monotone Nonsmooth Maps
Recent characterizations of various types of differentiable generalized monotone maps by Karamardian– Schaible–Crouzeix and their strengthened versions by Crouzeix–Ferland are extended to the nonsmooth case. For nondifferentiable locally Lipschitz maps necessary and/or sufficient conditions for quasimonotonicity, pseudomonotonicity and strict/ strong pseudomonotonicity are derived. To accomplis...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1986
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1986-0857953-x