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anything better - I might try "example" until someone does. I would hope that in future if anybody is still unhappy with my edit they would correct the bit they are unhappy with, rather than revert the good along with the bad - especially if the alternative POV is unfamiliar to them. I am not a very experienced editor, but I have tried to follow
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AIUI the projective line is NOT a topological circle: a circle is a metric object (distinct from, say, an ellipse) embedded in a metric plane, and it has a identifiable sides - inside and outside. A projective line need have no metric but, more importantly, even in the projective plane it has only
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I'm not arguing with you. I was just trying to imagine what the anonymous poster was objecting to/asking about. (I certainly walk around with a mindset so that whenever I read the word "topological", I assume the author implied "not smooth" as a corollary, unless stated otherwise. (This is a habit
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to be considered, however distasteful this might be to anyone personally. For this reason I will reinstate the bulk of my edit, but will delete the "metrical" reference. As for the "visualisation" aspect, I have always been unsure if this was the right word (see above) but nobody has suggested
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Thanks for the reply Mct mht, and for your high opinion of my abilities (actually you are right about the amateur bit, though I have apparently studied synthetic geometry in greater depth than some professionals; you might like to compare my comments with the approach taken in the main
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i was asked to respond in a edit summary. so i'll do it once. your comments are amateurish/crankish, both on my talk page and here. the edit you made was a minor one. it amounts to inserting the phrase "A (metrically) finite visualisation...", which, in this context, is garbage.
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has no metric and hence no concept of infinity. I would suggest that it be moved down to the section on the Real projective line, and the two statements be merged near the start of the section, something along the lines of; "It may be thought of as the real line
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I have to agree with Mct mht. It has been years and this article is still in poor condition. What is all this nonsense about projecting points in the plane onto the unit circle and identifying antipodal points, or quotienting out by a "subgroup" (subgroup of
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The same section also states, "One may also think of gluing the two "ends" of the real line onto a new point ∞ resulting in a circle." And in the introduction to the article, we find; "The projective line may also be thought of as the line
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with the unit circle and perform that identification (even though in the case of the 1-sphere, you happen to just get a 1-sphere back)? Better yet, just define it as the set of all lines through the origin in
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consider the projective line over a field as a special case of a projective line over a ring. In fact most people, that learn projective lines or work with them, never consider projective lines over a ring.
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points." This should more correctly begin with something like; "A (metrically) finite visualisation is obtained by ...", although I am not sure if "visualisation" is the correct word here. -- Cheers,
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the article should refer to everything that comes under its title. Therefore the lede and first section have been expanded in scope to include projective lines over not only fields, but also rings.
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one side. I would call it a topological loop (1-manifold) but not a circle. Or do topologists differ from other geometers in the sense that they give to the word "circle"? -- Cheers,
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in the definition of a projective line, so a link was restored today. Mention of "undue weight" demeans my contribution as "flat earth" advocacy. Note that I added three
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carry, then? (The answer is one and only one.) Don't confuse this with the gap between continuous and smooth mappings, which is a different point.
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to this article that is deficient in them, while the editor added none. His prejudice is evident in his final sentence above. Discussion expected.
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Saying something is diffeomorphically a circle is certainly stronger than saying it is topologically so.
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with the main contributor. I take the point about "metrically". But there is also an issue of
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from reading about ergodicity/chaos theory). Perhaps this is what anon was thinking too.)
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