search

sagemath / sage

Main repository of SageMath
https://www.sagemath.org
Other
1.43k stars 479 forks source link

Images of differentiable maps #31745

Open mkoeppe opened 3 years ago

mkoeppe commented 3 years ago

Images of differentiable maps from a domain to a higher-dimensional codomain cannot have a nonempty subset that is open in the codomain.

We define a subclass DiffMapImage of ContinuousMapImage (#31653) that declares open subsets as empty (#31732).

CC: @egourgoulhon @mjungmath @tscrim

Component: manifolds

Issue created by migration from https://trac.sagemath.org/ticket/31745

mkoeppe commented 3 years ago
comment:1

https://mathoverflow.net/questions/201424/proof-that-no-differentiable-space-filling-curve-exists, probably a better reference would be needed