A remark on the generalized Hodge conjecture.

It is well known that for a smooth, projective variety X over C the space of the coniveau filtration N^pH^i(X,Q) is contained in the intersection of the space of the Hodge filtration F^pH^i(X,C) with H^i(X,Q). In general this inclusion is strict. We introduce a natural subspace S^{p,i} of F^pH^i(X,C) such that for any integers i,p, N^pH^i(X,Q) is the intersection of S^{ p,i} with H^i(X,Q). The main technical tool is the use of semi-algebraic sets, which are available by the triangulation of complex projective varieties.