Daily Archives: May 3, 2016

Smooth Maps and the Category of Smooth Manifolds (Pt. III)

Originally posted on Abstract Nonsense:
Point of Post: This is a continuation of this post. Now, what we’d like to discuss is the set of all smooth functions (for us, when we remember, we shall obey history’s tough hand, and call…

Posted in Philosophie

Smooth Maps and the Category of Smooth Manifolds (Pt. II)

Originally posted on Abstract Nonsense:
Point of Post: This is a continuation of this post. Of course, most of the standard results about smooth functions in the Euclidean case transfer over to this general case. In particular: Theorem: Let be smooth manifolds…

Posted in Philosophie

Smooth Maps and the Category of Smooth Manifolds (Pt. I)

Originally posted on Abstract Nonsense:
Point of Post: In this post we define what it means for a map between two manifolds to be smooth. Motivation We literally defined smooth manifolds to be the topological spaces where we will have…

Posted in Philosophie