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There are other dimensions in which we can show the closedness if we replace Emb(R-j, R-n) by (Emb) over bar (R-j, R-n), the homotopy fiber of the inclusion Emb(R-j, R-n) hooked right arrow Imm(R-j, R-n). We also show that the closed forms obtained give rise to nontrivial cohomology classes, evaluating them on some cycles of Emb(R-j, R-n) and (Emb) over bar (R-j, R-n). 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There are other dimensions in which we can show the closedness if we replace Emb(R-j, R-n) by (Emb) over bar (R-j, R-n), the homotopy fiber of the inclusion Emb(R-j, R-n) hooked right arrow Imm(R-j, R-n). We also show that the closed forms obtained give rise to nontrivial cohomology classes, evaluating them on some cycles of Emb(R-j, R-n) and (Emb) over bar (R-j, R-n). 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