From wall spaces to CAT(0) cube complexes by Indira Chatterji and Graham Niblo (2003, revised 2004)

Author preprint: arxiv.org/abs/math/0309036v3

Full text: arxiv.org/pdf/math/0309036

Section 1, pages 2–3, defines finite-separation wallspaces and explicitly calls their wall-count function a pseudometric. The arXiv version is dated 4 October 2004; the PDF also displays a later compilation date, which is not used as publication metadata.