Steenrod homology and local connectedness

Abstract

Steenrod homology is used to explain results concerning L C n {\text {L}}{{\text {C}}^n} -divisors and one-point compactifications of L C n {\text {L}}{{\text {C}}^n} -spaces. It is shown that the one-point compactification w X wX of a locally compact metrizable space X X is hl c n {\text {hl}}{{\text {c}}^n} iff X X is hl c n {\text {hl}}{{\text {c}}^n} and its Steenrod k k th homology is finite generated for k ⩽ n k \leqslant n .