Talk:Cantor tree surface

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If the Cantor tree is homeomorphic to a subset of the sphere, how can it possibly have infinite genus?

Bad use of illustration and worse problems

The illustration of some aspect of the Alexander horned sphere is a particularly bad way to show the reader what the subject of this article looks like.

I am not opposed to including this interesting picture in the article ... towards the end. But if there is going to be just one illustration, there are pictures that are a great deal more useful for conveying what the Cantor tree surface looks like.

But even worse: This passage is at the beginning of the article:

"In dynamical systems, the Cantor tree is an infinite-genus surface homeomorphic to a sphere with a Cantor set removed. The blooming Cantor tree is a Cantor tree with an infinite number of handles added in such a way that every end is a limit of handles."

No. This misstates the names of these things. The "Cantor tree" is a tree — a one-dimensional complex, not a surface. The "Cantor tree surface" is the correct name for this surface.

I'm not even sure the "blooming Cantor tree surface" is an established name (outside of appearing in maybe one paper). In which case it does not belong in Wikipedia.

It is a very bad idea for a Wikipedia article on a mathematical subject to mislabel something. 2601:200:C000:1A0:9564:83C:87A8:95F4 (talk) 00:55, 27 June 2021 (UTC)[reply]