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Abstract and Applied Analysis
Volume 2013, Article ID 873943, 7 pages
Research Article

Ball-Covering Property in Uniformly Non- Banach Spaces and Application

1Department of Mathematics, Northeast Forestry University, Harbin 150040, China
2Department of Mathematics, Harbin University of Science and Technology, Harbin 150080, China

Received 7 September 2013; Revised 9 November 2013; Accepted 11 November 2013

Academic Editor: Khalil Ezzinbi

Copyright © 2013 Shaoqiang Shang and Yunan Cui. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper shows the following. (1) is a uniformly non- space if and only if there exist two constants such that, for every 3-dimensional subspace of , there exists a ball-covering of with or which is -off the origin and . (2) If a separable space has the Radon-Nikodym property, then has the ball-covering property. Using this general result, we find sufficient conditions in order that an Orlicz function space has the ball-covering property.