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The usual notion of Peano curve involves continuous images of the unit interval, not the whole real line (which could be considered as well, of course).
So I made some adjustments and stated some relevant facts at Peano curve, with a few pointers to proofs and to literature.
added cross-link with Giuseppe Peano (but haven’t dug out any original reference)
Added the original reference:
* [[Guiseppe Peano]], *Sur une courbe, qui remplit toute une aire plane*, Mathematische Annalen, **36** 1 (1890) 157–160 [[doi:10.1007/BF01199438](https://doi.org/10.1007/BF01199438)]
(Note that an HTML entity reference can be used to escape the first [)
Anonymous
Thanks! I have added the reference also to the entry Giuseppe Peano – here.
(I guess it must be “Giuseppe” not “Guiseppe”. Will need to fix our misspelled/duplicate entry, too…)
Finally, thanks for making the good point about the escaped character. The problem is that I won’t remember [
as well as $[$
, but I guess I should try. If only to stop Instiki from making a line break after the character. :-)
Added reference to Sagan’s 1994 Universitext Space-filling curves.
Sorry about the typo! I reckon [
is slightly cheaper than $[$
on the client side since it doesn’t get turned into MathJax (there’s apparently also [
according to §3.1 of the HTML spec). I tend to just copy the citation markup from the nForum thread to make absolutely sure it’s the same (esp. since the italicization is the other way round from APA style, Chicago style, MLA style, and ASA style).
Anonymous
Thanks for pointing out [
/]
, I had not thought of these. That should be a good compromise, I have recorded that here now.
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