Difference between revisions of "Lebesgue number"
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| − | The '''Lebesgue number''' of an [[open cover]] ''C'' of a metric space ''(X, d)'' is a real number <math>\delta > 0</math> such that if a subset ''A'' of ''X'' has diameter less than <math>\delta</math>, then ''A'' is contained in at least one element of ''C''. If ''X'' is [[ | + | The '''Lebesgue number''' of an [[open cover]] ''C'' of a metric space ''(X, d)'' is a real number <math>\delta > 0</math> such that if a subset ''A'' of ''X'' has diameter less than <math>\delta</math>, then ''A'' is contained in at least one element of ''C''. If ''X'' is [[compact space|compact]], then it has at least one Lebesgue number. |
[[category:topology]] | [[category:topology]] | ||
Revision as of 08:38, April 11, 2007
The Lebesgue number of an open cover C of a metric space (X, d) is a real number <math>\delta > 0</math> such that if a subset A of X has diameter less than <math>\delta</math>, then A is contained in at least one element of C. If X is compact, then it has at least one Lebesgue number.