let GX be TopSpace; :: thesis: for A being Subset of GX st A is connected holds
Cl A is connected
let A be Subset of GX; :: thesis: ( A is connected implies Cl A is connected )
assume A1: A is connected ; :: thesis: Cl A is connected
( A c= Cl A & Cl A c= Cl A ) by PRE_TOPC:48;
hence Cl A is connected by A1, Th19; :: thesis: verum