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Results tagged with gn.general-topology
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user 1468
Continuum theory, point-set topology, spaces with algebraic structure, foundations, dimension theory, local and global properties.
0
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Can connectedness of fibers of a smooth map be checked on a dense set?
I think in general it can not be checked on a dense set. Consider the normalization map from a smooth curve to a nodal curve, for example, a natural smooth surjection you can come up with from S^1 to …
- 377
0
votes
Convexity Theorem of Hamiltonian actions - the connectedness part
The first question is OK, i.e., the fiber of \eta is indeed connected for every regular value \eta, since it is like a product here - please refer to Ehresmann's Theorem and also a related post "Can c …
- 377
2
votes
4
answers
626
views
Can connectedness of fibers of a smooth map be checked on a dense set?
Suppose $f: M\to N$ is a smooth map between two smooth manifolds, with $M$ compact and connected, and suppose there is a dense subset of $f(M)$ where each fiber is connected, then each fiber of $f$ is …
- 377
2
votes
2
answers
305
views
Convexity Theorem of Hamiltonian actions - the connectedness part
Suppose we have a Hamiltonian action of a torus $T = T^m = R^m/Z^m$ on a compact, connected symplectic manifold $M$. According to the convexity theorem, we know every fiber of the momentum map $\mu: M …
- 377