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Covering Dimension from Large Sets
Author(s) -
STONE A.H.
Publication year - 1996
Publication title -
annals of the new york academy of sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.712
H-Index - 248
eISSN - 1749-6632
pISSN - 0077-8923
DOI - 10.1111/j.1749-6632.1996.tb49186.x
Subject(s) - dimension (graph theory) , ball (mathematics) , cube (algebra) , metric space , mathematics , combinatorics , metric (unit) , pure mathematics , geometry , engineering , operations management
The notion of “covering dimension” involves coverings by “small enough” sets; how small is “enough” is investigated for the n ‐cube and spherical n ‐ball. The results are applied to give a partial answer to a question of J. Tišer about the existence of σ‐discrete open covers of metric spaces ( X , ρ) in which the n ‐th discrete system consists of sets of small diameters.