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K-cell (mathematics) : ウィキペディア英語版 | K-cell (mathematics)
A ''k''-cell is a higher-dimensional version of a rectangle or rectangular solid. It is the Cartesian product of ''k'' closed intervals on the real line. This essentially means that is a ''k''-dimensional rectangular solid, with each of its edges being equal to one of the closed intervals used in the definition. The ''k'' intervals need not be identical. For example, a 2-cell is a rectangle in such that the sides of the rectangles are parallel to the coordinate axes. == Formal definition ==
Let ''a''''i'' ∈ and ''b''''i'' ∈ . If ''a''''i'' < ''b''''i'' for all ''i'' = 1,...,''k'', the set of all points x = (''x''1,...,''x''''k'') in whose coordinates satisfy the inequalities ''a''i ≤ ''x'' ≤ ''b''''i'' is a ''k''-cell.〔Rudin, W: ''Principles of Mathematical Analysis'', page 31. McGraw-Hill, 1976.〕 Every ''k''-cell is compact.〔Rudin, W: ''Principles of Mathematical Analysis'', page 39. McGraw-Hill, 1976.〕
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