Some geometric and topological properties of Banach spaces via ball coverings |
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Authors: | Lixin Cheng Yu Zhou |
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Institution: | School of Mathematical Sciences, Xiamen University, Xiamen 361005, China |
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Abstract: | By a ball-covering B of a Banach space X, we mean that B is a collection of open (or closed) balls off the origin whose union contains the unit sphere of X; and X is said to have the ball-covering property provided it admits a ball-covering of countably many balls. This paper shows that Gδ property of points in a Banach space X endowed with the ball topology is equivalent to the space X admitting the ball-covering property. Moreover, smoothness, uniform smoothness of X can be characterized by properties of ball-coverings of its finite dimensional subspaces. |
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Keywords: | Ball-covering Ball-topology Smoothness Banach space |
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