A classification for non-linearly bounded convex sets

1993 ◽  
Vol 61 (6) ◽  
pp. 576-583
Author(s):  
J. Bair ◽  
J. L. Valein
Keyword(s):  
Convex Sets ◽  
Bounded Convex

scholarly journals About an Erdős–Grünbaum Conjecture Concerning Piercing of Non-bounded Convex Sets

2015 ◽  
Vol 53 (4) ◽  
pp. 941-950
Author(s):  
Amanda Montejano ◽  
Luis Montejano ◽  
Edgardo Roldán-Pensado ◽  
Pablo Soberón
Keyword(s):  
Convex Sets ◽  
Bounded Convex

On the Vector Sum of Two Convex Sets in Space

1991 ◽  
Vol 43 (2) ◽  
pp. 347-355 ◽  
Author(s):  
Steven G. Krantz ◽  
Harold R. Parks
Keyword(s):  
Convex Sets ◽  
Analytic Boundary ◽  
Real Analytic ◽  
Vector Sum ◽  
Bounded Convex

In the paper [KIS2], C. Kiselman studied the boundary smoothness of the vector sum of two smoothly bounded convex sets A and B in . He discovered the startling fact that even when A and B have real analytic boundary the set A + B need not have boundary smoothness exceeding C20/3 (this result is sharp). When A and B have C∞ boundaries, then the smoothness of the sum set breaks down at the level C5 (see [KIS2] for the various pathologies that arise).

Order cancellation law in the family of bounded convex sets

2019 ◽  
Vol 77 (2) ◽  
pp. 289-300
Author(s):  
J. Grzybowski ◽  
R. Urbański
Keyword(s):  
Convex Sets ◽  
The Family ◽  
Bounded Convex

scholarly journals Ul’yanov-type inequality for bounded convex sets in Rd

2008 ◽  
Vol 151 (1) ◽  
pp. 60-85 ◽  
Author(s):  
Z. Ditzian ◽  
A. Prymak
Keyword(s):  
Convex Sets ◽  
Type Inequality ◽  
Bounded Convex

scholarly journals The completeness of a normed space is equivalent to the homogeneity of its space of closed bounded convex sets

2013 ◽  
Vol 5 (1) ◽  
pp. 44-46
Author(s):  
I. Hetman
Keyword(s):  
Normed Space ◽  
Convex Sets ◽  
Infinite Dimensional ◽  
Dimensional Normed Space ◽  
Bounded Convex ◽  
Convex Subsets

We prove that an infinite-dimensional normed space $X$ is complete if and only if the space $\mathrm{BConv}_H(X)$ of all non-empty bounded closed convex subsets of $X$ is topologically homogeneous.

On Super Weakly Compact Convex Sets and Representation of the Dual of the Normed Semigroup They Generate

2013 ◽  
Vol 56 (2) ◽  
pp. 272-282 ◽  
Author(s):  
Lixin Cheng ◽  
Zhenghua Luo ◽  
Yu Zhou
Keyword(s):  
Banach Space ◽  
Convex Sets ◽  
Convex Set ◽  
Compact Convex ◽  
Lower Semicontinuous ◽  
Weakly Compact ◽  
Bounded Set ◽  
Fréchet Differentiable ◽  
Bounded Convex

AbstractIn this note, we first give a characterization of super weakly compact convex sets of a Banach space X: a closed bounded convex set K ⊂ X is super weakly compact if and only if there exists a w* lower semicontinuous seminorm p with p ≥ σK ≌ supxєK 〈.,x〉 such that p2 is uniformly Fréchet differentiable on each bounded set of X*. Then we present a representation theoremfor the dual of the semigroup swcc(X) consisting of all the nonempty super weakly compact convex sets of the space X.

scholarly journals Characterisation of drop and weak drop properties for closed bounded convex sets

1991 ◽  
Vol 43 (3) ◽  
pp. 377-385 ◽  
Author(s):  
J.R. Giles ◽  
Denka N. Kutzarova
Keyword(s):  
Convex Sets ◽  
Drop Theorem ◽  
Bounded Convex

Modifying the concept underlying Daneš' drop theorem, Rolewicz introduced the notion of the drop property of a norm which was later generalised to the weak drop property of a norm. Kutzarova extended the discussion to consider the drop property for closed bounded convex sets. Here we characterise the drop and weak drop properties for such sets by upper semi-continuous and compact valued subdifferential mappings.

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