Based　on　the　independent,　continuous　and　mapping　(ICM)　method　and　homogenization　method,　a　research　model　is　constructed　to　propose　and　deduce　a　theorem　and　corollary　from　the　invariant　between　the　weight　filter　function　and　the　corresponding　stiffness　filter　function　of　the　form　of　power　function.　The　efficiency　in　searching　for　optimum　solution　will　be　raised　via　the　choice　of　rational　filter　functions,　so　the　above　mentioned　results　are　very　important　to　the　further　study　of　structural　topology　optimization.