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P1: A curve defines a vector at point.
P2: A function defines a covector at a point.
F1a: A congruence of curves defines a vector field.
F1b:Every vector field corresponds to a congruence of curves.
Statements F1 are analogous to P1.
F2a: A "congruence of functions" defines a covector field?
F2b: Every covector field correspond to a "congruence of functions"?
What, if any, are the correct statements F2 that would be analogous to P2, just as F1 is analogous to P1?
P2: A function defines a covector at a point.
F1a: A congruence of curves defines a vector field.
F1b:Every vector field corresponds to a congruence of curves.
Statements F1 are analogous to P1.
F2a: A "congruence of functions" defines a covector field?
F2b: Every covector field correspond to a "congruence of functions"?
What, if any, are the correct statements F2 that would be analogous to P2, just as F1 is analogous to P1?