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Continuum theory, point-set topology, spaces with algebraic structure, foundations, dimension theory, local and global properties.

0 votes
0 answers
73 views

Can we construct general counterexample to support the Weak Whitney theorem? [duplicate]

Can we construct an example for the weak Whitney theorem to illustrate the existence of a continuous function from an $n$-dimensional manifold to an $m$-dimensional manifold that cannot be smoothly em …
li ang Duan's user avatar
1 vote
0 answers
126 views

Can we construct a general counterexample to support the weak whitney embedding theorm?

The weak Whitney embedding theorem states that any continuous function from an $n$-dimensional manifold to an $m$-dimensional manifold may be approximated by a smooth embedding provided $m > 2n$. Some …
li ang Duan's user avatar
1 vote
1 answer
188 views

Can orientation preserving diffeomorphism in $\mathbb{R}^d$ be presented by flowmap of dynam...

Because flowmaps are homeomorphic maps, I was wondering if there is any literature that proves that diffeomorphism $\Phi(x)$ can be expressed as a flowmap of a certain dynamical system? that is, does …
li ang Duan's user avatar