scholarly journals Cells and Cellularity in Infinite-Dimensional Normed Linear Spaces

1973 ◽  
Vol 176 ◽  
pp. 401
Author(s):  
R. A. Mc Coy
Keyword(s):  
Linear Spaces ◽  
Infinite Dimensional ◽  
Normed Linear Spaces

Gaps between Spheres in Normed Linear Spaces

1980 ◽  
Vol 23 (3) ◽  
pp. 347-354 ◽  
Author(s):  
Robert H. Lohman
Keyword(s):  
Linear Space ◽  
Normed Linear Space ◽  
Linear Spaces ◽  
Infinite Dimensional ◽  
Normed Linear Spaces ◽  
Concentric Spheres ◽  
General Conditions

AbstractThe geometric notions of a gap and gap points between “concentric” spheres in a normed linear space are introduced and studied. The existence of gap points characterizes finitedimensional spaces. General conditions are given under which an infinite-dimensional normed linear space admits concentric spheres such that both these spheres and their dual spheres fail to have gap points.

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