cianfa72's latest activity
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cianfa72 reacted to PeterDonis's post in the thread Undergrad Physical Interpretation of Frame Field with
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Yes. That's the only orthogonality condition we've discussed. -
cianfa72 reacted to PeterDonis's post in the thread Undergrad Physical Interpretation of Frame Field with Like.
A set of points forming a one-dimensional curve. But that's because you specified the orthogonality condition. If you don't specify the...
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cianfa72 reacted to PeterDonis's post in the thread Undergrad Physical Interpretation of Frame Field with Like.
Note that this "exponentiation" operation isn't really well-defined, rigorously speaking, because it treats tangent vectors as...
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cianfa72 reacted to PeterDonis's post in the thread Undergrad Physical Interpretation of Frame Field with Like.
As long as it's a sufficiently small length compared with the scale of the spacetime curvature.
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cianfa72 posted the thread Undergrad Physical Interpretation of Frame Field in Special and General Relativity.Moderator's note: Spin-off from another thread due to topic change. In the second link referenced, there is a claim about a physical...
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cianfa72 reacted to lavinia's post in the thread Undergrad 2-sphere intrinsic definition by gluing disks' boundaries with Like.
In the category of topological spaces and homeomorphisms, one can define those manifolds which are made from gluing two disks along...
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cianfa72 reacted to fresh_42's post in the thread Undergrad About the definition of topological manifold using closed sets with Like.
The key point is that you can choose whatever small neighborhood around a point and still have the same behavior. A closed set might...
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cianfa72 replied to the thread Undergrad About the definition of topological manifold using closed sets.Ah yes, well spotted. The same issue doesn't occur when using open sets to define neighborhoods. So, by using closed sets, we no longer...
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cianfa72 reacted to martinbn's post in the thread Undergrad About the definition of topological manifold using closed sets with
Informative.
Let's take our topological space to be the plane ##M=\mathbb R^2##. How do you make it a topological manifold using closed sets? Every... -
cianfa72 replied to the thread Undergrad About the definition of topological manifold using closed sets.Use this -- Definition using closed sets. The definition of chart ##(U, \phi)## is based on closed sets using homemorphism on the image...
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cianfa72 replied to the thread Undergrad About the definition of topological manifold using closed sets.Define the topologies involved by using axioms for closed sets (i.e. arbitrary intersections and finite unions instead of vice versa)...
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cianfa72 replied to the thread Undergrad About the definition of topological manifold using closed sets.Sorry, can you better explain what is the trouble with singletons set ?
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cianfa72 replied to the thread Undergrad About the definition of topological manifold using closed sets.Nothing. I asked it just to better understand how topological vs differential elements enter the definition of manifold (topological vs...
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cianfa72 posted the thread Undergrad About the definition of topological manifold using closed sets in Topology and Analysis.We all know the definition of n-dimensional topological manifold uses open sets and homeomorphisms onto the image as open set in...
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cianfa72 replied to the thread Undergrad About the maximal extension of local charts on a manifold.In the first case (rational ratio) vector fields ##(1,2)## and ##(3,4)## are smooth, pointwise linearly independent, commute and their...