Are the two definitions of differentiable structure on $M$ not equivalent?
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The following pages are from Lee's "Introduction to smooth manifolds".
The following pages are from Varadarajan's "Lie Groups, Lie Algebras, and Their Representations".
I think the two definitions of ($C^infty$) differentiable structure on $M$ in the two books are not equivalent, isn't it?
manifolds lie-groups lie-algebras smooth-manifolds
asked Nov 23 at 3:21
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The following pages are from Lee's "Introduction to smooth manifolds".
The following pages are from Varadarajan's "Lie Groups, Lie Algebras, and Their Representations".
I think the two definitions of ($C^infty$) differentiable structure on $M$ in the two books are not equivalent, isn't it?
manifolds lie-groups lie-algebras smooth-manifolds
asked Nov 23 at 3:21
Born to be proud
782510
1
You should point out specifics of where you think that the two definitions differ. Giving an example of a structure which satisfies one set of axioms but not the other would be very helpful (but perhaps not doable).
– Joppy
Nov 23 at 12:08
The two definitions are quite different and it's not clear how to connect one to the other, so I think the question is justified.
– Junyan Xu
Nov 25 at 21:14
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
The following pages are from Lee's "Introduction to smooth manifolds".
The following pages are from Varadarajan's "Lie Groups, Lie Algebras, and Their Representations".
I think the two definitions of ($C^infty$) differentiable structure on $M$ in the two books are not equivalent, isn't it?
manifolds lie-groups lie-algebras smooth-manifolds
asked Nov 23 at 3:21
Born to be proud
782510
The following pages are from Lee's "Introduction to smooth manifolds".
The following pages are from Varadarajan's "Lie Groups, Lie Algebras, and Their Representations".
I think the two definitions of ($C^infty$) differentiable structure on $M$ in the two books are not equivalent, isn't it?
manifolds lie-groups lie-algebras smooth-manifolds
manifolds lie-groups lie-algebras smooth-manifolds
asked Nov 23 at 3:21
Born to be proud
782510
asked Nov 23 at 3:21
Born to be proud
782510
asked Nov 23 at 3:21
Born to be proud
782510
asked Nov 23 at 3:21
Born to be proud
782510
asked Nov 23 at 3:21
Born to be proud
782510
782510
1
You should point out specifics of where you think that the two definitions differ. Giving an example of a structure which satisfies one set of axioms but not the other would be very helpful (but perhaps not doable).
– Joppy
Nov 23 at 12:08
The two definitions are quite different and it's not clear how to connect one to the other, so I think the question is justified.
– Junyan Xu
Nov 25 at 21:14
add a comment |
1
You should point out specifics of where you think that the two definitions differ. Giving an example of a structure which satisfies one set of axioms but not the other would be very helpful (but perhaps not doable).
– Joppy
Nov 23 at 12:08
The two definitions are quite different and it's not clear how to connect one to the other, so I think the question is justified.
– Junyan Xu
Nov 25 at 21:14
1
1
You should point out specifics of where you think that the two definitions differ. Giving an example of a structure which satisfies one set of axioms but not the other would be very helpful (but perhaps not doable).
– Joppy
Nov 23 at 12:08
You should point out specifics of where you think that the two definitions differ. Giving an example of a structure which satisfies one set of axioms but not the other would be very helpful (but perhaps not doable).
– Joppy
Nov 23 at 12:08
The two definitions are quite different and it's not clear how to connect one to the other, so I think the question is justified.
– Junyan Xu
Nov 25 at 21:14
The two definitions are quite different and it's not clear how to connect one to the other, so I think the question is justified.
– Junyan Xu
Nov 25 at 21:14
add a comment |
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1
You should point out specifics of where you think that the two definitions differ. Giving an example of a structure which satisfies one set of axioms but not the other would be very helpful (but perhaps not doable).
– Joppy
Nov 23 at 12:08
The two definitions are quite different and it's not clear how to connect one to the other, so I think the question is justified.
– Junyan Xu
Nov 25 at 21:14