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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 [[|compact space|compact]], then it has at least one Lebesgue number.

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]]