theorem Th2: :: TOPS_3:2

for X being TopStruct
for A being Subset of X holds
( ( A = [#] X implies A ` = {} X ) & ( A ` = {} X implies A = [#] X ) & ( A = the carrier of X implies A ` = {} ) & ( A ` = {} implies A = the carrier of X ) ) by XBOOLE_1:37;