Differential geometry uses the techniques of differential calculus,
integral calculus, linear algebra
and multilinear algebra to study problems in geometry.
Differential geometry has grown into a field concerned with
the geometric structures on differentiable manifolds
and closely related to differential topology and the geometric aspects of
the theory of differential equations.
General topology (point-set topology)
The fundamental concepts in point-set topology are continuity,
compactness, and connectedness:
Continuous functions, intuitively, take nearby points to nearby points.
Compact sets are those that can be covered by finitely many sets of arbitrarily small size.
Connected sets are sets that cannot be divided into two pieces that are far apart.
Wiki
|