I'm not even sure if the archetypical Cantor set should be described as a "collection of zero-dimensional points", except in the sense that *every * point
Sorry, I left out the word "disconnected" (spatially not functionally) and although you're correct about the non-isolated nature of the Cantor Set itself, that doesn't apply to the full generalisation of Cantor Dusts and certainly not to non-infinite dusts (i.e. with a finite number of separate disconnected parts). On 26 Feb 2014, at 00:01, Allan Wechsler wrote:
I'm not even sure if the archetypical Cantor set should be described as a "collection of zero-dimensional points", except in the sense that *every * point set is such a collection. No element of the Cantor set is isolated, in the sense that every neighborhood of a point in the Cantor set also contains other points in the set.
On Tue, Feb 25, 2014 at 6:08 PM, David Makin <makinmagic@tiscali.co.uk>wrote:
Just to add - attractors classified as "Cantor dust" do not solely consist of collections of zero-dimensional points like the Cantor Set, Cantor Dust attractors include those consisting of separate parts each of which can be of any dimensionality.
On 25 Feb 2014, at 23:00, David Makin wrote:
Consider quantum entanglement in terms of disconnected attractors - a form of Cantor Dust, - so even though physically distant they are still part of a single mathematical function/system/process..
On 25 Feb 2014, at 22:30, Warren D Smith wrote:
I'm unsure whether this idea is completely insane:
https://www.sciencenews.org/article/quantum-timekeeping
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