Let $L$ be any language. Define even $(w)$ as the string obtained by extracting from $w$ the letters in even$-$numbered positions; that is$,$ if

$w=a_1{a}_2{a}_3{a}_{4.....}$

then

even $(w)=a_2{a}_4.....$

Corresponding to this, we can define a language

even $(L)=\{even(w)$:winL$\}.$