let T be TopSpace; :: thesis: for A being Subset of T holds
( A is condensed iff ( Int A is regular_open & Cl A is regular_closed & Border A is empty ) )
let A be Subset of T; :: thesis: ( A is condensed iff ( Int A is regular_open & Cl A is regular_closed & Border A is empty ) )
thus ( A is condensed implies ( Int A is regular_open & Cl A is regular_closed & Border A is empty ) ) by Th25, Th26; :: thesis: ( Int A is regular_open & Cl A is regular_closed & Border A is empty implies A is condensed )
assume ( Int A is regular_open & Cl A is regular_closed & Border A is empty ) ; :: thesis: A is condensed
then ( A is supercondensed & A is subcondensed ) by Th25, Th26;
hence A is condensed ; :: thesis: verum