Talk:Dogbone space

What is a generalized homological manifold? Is the dogbone space a homology manifold?

The page states that Bing's dogbone space is a 'generalized homological manifold'. Google Scholar does have a few viewable hits for "generalized homology manifold". I'm wondering if in fact the dogbone space is a homology manifold, and that the page should instead assert this. In a review of Bing's paper A decomposition of E3 into points and tame arcs such that the decomposition space is topologically different from E3, by E. E. Moise, the following is stated:

It follows from a theorem of R. L. Wilder [Pacific J. Math. 7 (1957), 1519–1528; MR0092966 (19,1188e)] that, since the natural projection π: E3 → G is monotonic in every dimension, G must be a generalized (homological) three-manifold. And it has been shown by M. L. Curtis and R. L. Wilder [Bull. Amer. Math. Soc. 62 (1956), 180] that such a G must also be a homotopy manifold. Thus the stated property of G is an extremely delicate property. The construction of the example, and the preliminary steps in the proof, are too technical for a brief summary.

I don't actually know if the G appearing here is Bing's dogbone space. Since the Wikipedia article asserts that Bing's dogbone space is both a homotopy manifold and a generalized homological manifold, and Bing's papers don't use the terminology of 'generalized homological manifold', I'm guessing this is the source of that claim. 2600:387:3:805:0:0:0:67 (talk) 15:30, 28 May 2025 (UTC)