Talk:Projective line

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"Topologically, it is again a circle." Is the real projective line not also a circle in terms of differentiable manifolds? 145.97.196.54 17:42, 12 January 2006 (UTC)

Well, yes, that follows. Charles Matthews 17:58, 12 January 2006 (UTC)

Saying something is diffeomorphically a circle is certainly stronger than saying it is topologically so. linas 00:00, 13 January 2006 (UTC)

Really. So how many smooth structures does the circle as topological manifold 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. Charles Matthews 08:16, 13 January 2006 (UTC)

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 from reading about ergodicity/chaos theory). Perhaps this is what anon was thinking too.) linas 01:35, 14 January 2006 (UTC)