It is shown that the statements:{\it Compact } $T_{2}$ 

 {\it spaces are weakly Loeb }and {\it the product of weakly Loeb } 

$T_{2}$ {\it spaces isweakly Loeb} are not provable in $ZF^{0},$ 

Zermelo-Fraenkel set theorywithout the axiom of regularity.