Lindel\"of space Lindelof 2002-01-04 18:36:46 2007-05-23 13:50:24 Definition Lindel\"of Lindel\"of property topology \section*{Definition} A topological space is said to be \emph{Lindel\"of} if every open cover has a countable subcover. \section*{Notes} A second-countable space is Lindel\"of. A compact space is Lindel\"of. A \PMlinkname{regular}{T3Space} Lindel\"of space is \PMlinkid{normal}{1530}. \PMlinkname{$F_\sigma$ sets}{F_sigmaSet} in Lindel\"of spaces are Lindel\"of. Continuous images of Lindel\"of spaces are Lindel\"of. A Lindel\"of space is compact if and only if it is countably compact.