Some remarks on measures of noncompactness and retractions onto spheres
نویسندگان
چکیده
منابع مشابه
Some Remarks on Output Measures
An output measure is an image of a uniform Bernoulli measure on finitely many states. We discuss “generalized Bernoulli” measures of [F-J], and answer several questions posed in that paper, in particular we establish a condition when such a measure is a finitary output measure. Answering D. Goldstein’s question, we characterize output measures via block codes in terms of walks on labeled graphs...
متن کاملInequivalent measures of noncompactness
Two homogeneous measures of noncompactness β and γ on an infinite dimensional Banach space X are called “equivalent” if there exist positive constants b and c such that bβ(S) ≤ γ (S) ≤ cβ(S) for all bounded sets S ⊂ X . If such constants do not exist, the measures of noncompactness are “inequivalent.”Weask a foundational questionwhich apparently has not previously been considered: For what infi...
متن کاملSome Remarks about Lie Groups Transitive on Spheres and Tori
The present note pertains principally to two papers of D. Montgomery and H. Samelson [l, 2J, in which the authors study compact Lie groups transitive on tori [ l ] and spheres [2], I will here prove in another way, generalize, and sharpen a part of their results. §1 contains the remarks to [ l ] , §2 to [2]; they are independent of one another and the methods used in both are quite different. I...
متن کاملRetractions onto series-parallel posets
The poset retraction problem for a poset P is whether a given poset Q containing P as a subposet admits a retraction onto P, that is, whether there is a homomorphism from Q onto P which fixes every element of P. We study this problem for finite series-parallel posets P. We present equivalent combinatorial, algebraic, and topological charaterisations of posets for which the problem is tractable,...
متن کاملOn Continuous Choice of Retractions onto Nonconvex Subsets
For a Banach space B and for a class A of its bounded closed retracts, endowed with the Hausdorff metric, we prove that retractions on elements A ∈ A can be chosen to depend continuously on A, whenever nonconvexity of each A ∈ A is less than 1 2 . The key geometric argument is that the set of all uniform retractions onto an α−paraconvex set (in the spirit of E. Michael) is α 1−α −paraconvex sub...
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: Topology and its Applications
سال: 2007
ISSN: 0166-8641
DOI: 10.1016/j.topol.2007.07.002