Set-Valued Generalizations of Baire′s Category Theorem
نویسندگان
چکیده
منابع مشابه
A Sard Theorem for Set-Valued Mappings∗†
If F is a set-valued mapping from IRn into IRm with closed graph, then y ∈ IRm is a critical value of F if for some x with y ∈ F (x), F is not metrically regular at (x, y). We prove that the set of critical values of a set-valued mapping whose graph is a definable (tame) set in an o-minimal structure containing additions and multiplications is a set of dimension not greater than m − 1 (resp. a ...
متن کاملGeneralizations of Hedberg's Theorem
As the groupoid interpretation by Hofmann and Streicher shows, uniqueness of identity proofs (UIP) is not provable. Generalizing a theorem by Hedberg, we give new characterizations of types that satisfy UIP. It turns out to be natural in this context to consider constant endofunctions. For such a function, we can look at the type of its fixed points. We show that this type has at most one eleme...
متن کاملSet-valued differentials and a nonsmooth version of Chow’s Theorem
In this note we present a simple application of the method developed by one of us in recent years to prove general smooth, nonsmooth, high-order, and hybrid versions of the maximum principle (abbr. MP) for finitedimensional, deterministic optimal control problems without state space constraints. As explained in Sussmann [3, 4, 5, 6], such versions can be derived in a unified way, by using a mod...
متن کاملAumann Type Set-valued Lebesgue Integral and Representation Theorem
In this paper, we shall firstly illustrate why we should discuss the Aumann type set-valued Lebesgue integral of a set-valued stochastic process with respect to time t under the condition that the set-valued stochastic process takes nonempty compact subset of d-dimensional Euclidean space. After recalling some basic results about set-valued stochastic processes, we shall secondly prove that the...
متن کاملAn Inverse Mapping Theorem for Set-valued Maps
We prove that certain Lipschitz properties of the inverse F-1 of a set-valued map F are inherited by the map (f+F)~x when / has vanishing strict derivative. In this paper, we present an inverse mapping theorem for set-valued maps F acting from a complete metric space I toa linear space Y with a (translation) invariant metric. We prove that, for any function f: X -> Y with "vanishing strict deri...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 1995
ISSN: 0022-247X
DOI: 10.1006/jmaa.1995.1387