The Alexander duality Theorem is usually stated for a triangulable pair $(\mathbb S^n, Y)$ where $Y$ is a subset of the standard sphere $\mathbb S^n$. My question is: Does the duality also hold if we rather replace $\mathbb S^n$ by a compact orientable Homology sphere (without boundary) (https://en.m.wikipedia.org/wiki/Homology_sphere) ? I'm mainly interested in the cases $n=2$ and $3$. I'm willing to assume that the Homology sphere is the Geometric realization of a finite abstract simplicial complex (https://en.m.wikipedia.org/wiki/Abstract_simplicial_complex)

Thanks