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On inclusion and summands of bounded closed convex sets
Authors:
- Jerzy Grzybowski,
- Ryszard Henryk Urbański
Abstract
It is proved that if the nonempty intersection of bounded closed convex sets A∩B is contained in (A ∩+ F) ∪ (B + F) and one of the following holds true: (i) the space X is less-than-three dimensional, (ii) A ∪ B is convex, (iii) F is a one-point set, then A ∩ B ⊂ A + F or A ∩ B ⊂ B + F (Theorems 2 and 3). Moreover, under some hypotheses the characterization of A and B such that A ∩ B is a summand of A ∪ B is given (Theorem 3). © 2005 Akadémiai Kiadó, Budapest.
- Record ID
- UAMae14f963c93f480697c627eefc689930
- Author
- Journal series
- Acta Mathematica Hungarica, ISSN 0236-5294
- Issue year
- 2005
- Vol
- 106
- Pages
- 293-300
- ASJC Classification
- DOI
- DOI:10.1007/s10474-005-0020-6 Opening in a new tab
- Language
- (en) English
- Score (nominal)
- 0
- Score source
- journalList
- Publication indicators
- = 4; = 4; : 2005 = 1.024; : 2006 (2 years) = 0.384 - 2007 (5 years) =0.402
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- Uniform Resource Identifier
- https://researchportal.amu.edu.pl/info/article/UAMae14f963c93f480697c627eefc689930/
- URN
urn:amu-prod:UAMae14f963c93f480697c627eefc689930
* presented citation count is obtained through Internet information analysis and it is close to the number calculated by the Publish or PerishOpening in a new tab system.