To formulate our results let M be a metric space with at least two points and let Y be a subspace of a generalized ordered (GO) space X. We get the following conclusions: If Cp(Y,M) admits a continuous injection into Cp(τ,M) for some ordinal τ, then Y¯∖Y is hereditarily paracompact. This generalizes some known conclusions. If Cp(Y,M) admits a continuous injection into Cp(Z,M) for a separable space Z, then Y¯∖Y is hereditarily paracompact. If Cp(Y,M) admits a continuous injection into Cp(L,M) for a linearly ordered compactum L which satisfies that 1-cf(minL)≥ω1, 0-cf(maxL)≥ω1, and i-cf(x)≥ω1 for x∈L∖{maxL,minL} and for i∈{0,1}, then Y¯∖Y is hereditarily paracompact.