 Here "reasonable" means "X" is locally contractible, σ-compact, and of finite dimension.In more detail, let formula_4 be the abelian group of formal (infinite) sums

where σ runs over the set of all continuous maps from the standard "i"-simplex Δ"i" to "X" and each "a"σ is an integer, such that for each compact subset "S" of "X", only finitely many maps σ whose image meets "S" have nonzero coefficient in "u".Then the usual definition of the boundary ∂ of a singular chain makes these abelian groups into a chain complex