second countableSecondCountable2002-01-01 22:13:312008-09-12 11:40:22Definition\usepackage{amssymb}
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\usepackage{xypic}A topological space is said to be \emph{second \PMlinkescapetext{countable}} if it has a countable \PMlinkname{basis}{BasisTopologicalSpace}.
It can be shown that a \PMlinkescapetext{second countable} space is both Lindel\"of and separable, although the converses fail. For instance, the lower limit topology on the real line is both Lindel\"of and separable, but not second countable.