The generalised (uniform) Mazur Intersection Property
نویسندگان
چکیده
Given a family C of closed bounded convex sets in Banach space X, we say that X has the C-MIP if every C∈C is intersection balls containing it. In this paper, introduce stronger version and show it more satisfactory generalisation MIP inasmuch as one can obtain complete analogues various characterisations MIP. We also uniform versions (strong) characterise them analogously. Even case, strong C-UMIP appears to have richer than C-UMIP.
منابع مشابه
The Mazur Intersection Property and Farthest Points
K. S. Lau had shown that a reflexive Banach space has the Mazur Intersection Property (MIP) if and only if every closed bounded convex set is the closed convex hull of its farthest points. In this work, we show that in general this latter property is equivalent to a property stronger than the MIP. As corollaries, we recapture the result of Lau and characterize the w*-MIP in dual of RNP spaces.
متن کاملMazur Intersection Property for Asplund Spaces
The main result of the present note states that it is consistent with the ZFC axioms of set theory (relying on Martin’s Maximum MM axiom), that every Asplund space of density character ω1 has a renorming with the Mazur intersection property. Combined with the previous result of Jiménez and Moreno (based upon the work of Kunen under the continuum hypothesis) we obtain that the MIP renormability ...
متن کاملA Note on Porosity and the Mazur Intersection Property
Let M be the collection of all intersections of balls, considered as a subset of the hyperspace H of all closed, convex and bounded sets of a Banach space, furnished with the Hausdorff metric. We prove that M is uniformly very porous if and only if the space fails the Mazur intersection property.
متن کاملModules with copure intersection property
In this paper, we investigate the modules with the copure intersection property and obtained obtain some related results.
متن کاملConnectivity of the uniform random intersection graph
A uniform random intersection graph G(n,m, k) is a random graph constructed as follows. Label each of n nodes by a randomly chosen set of k distinct colours taken from some finite set of possible colours of size m. Nodes are joined by an edge if and only if some colour appears in both their labels. These graphs arise in the study of the security of wireless sensor networks, in particular when m...
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: 2023
ISSN: ['0022-247X', '1096-0813']
DOI: https://doi.org/10.1016/j.jmaa.2023.127001