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I am pretty sure that the author(s) of this page are being a little sloppy here (and elsewhere) and that the geometric operations are restricted to distinct elements (semi mentioned in the lead, but dropped in the formal definition). I don't know what to say about "hence". I am not familiar with this
375:. There, the definition requires also that the incidence relation is a smooth embedded manifold. Is this requirement missing here? Also, there compactness is just required by definition (for being called "topological", the more so, "smooth"); and what happens here?
465:"The point manifold of a smooth projective plane is homeomorphic to its classical counterpart, and so is the line manifold." — Also not a part of the definition. And, according to McKay, they are (moreover) diffeomorphic.
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each smooth plane is a compact topological plane." — This "hence" is unclear to me. An immediate consequence? Or application of a nontrivial result well-known to experts?
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447:" — Not a part of the definition, rather, a theorem. McKay attributes this theorem to Freidenthal; or is it a
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material and am just trying to put this page into an acceptable WP format. --
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I guess, the operations of joining and intersecting are (defined and) smooth
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I am not familiar, too; this is why I just ask questions. I continue:
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