Mathcenter Forum - Differential Geometry กับ Elementary Topology อะไรยากกว่ากัน

Mathcenter Forum (https://www.mathcenter.net/forum/index.php)

- ปัญหาคณิตศาสตร์ทั่วไป (https://www.mathcenter.net/forum/forumdisplay.php?f=1)

Differential Geometry กับ Elementary Topology อะไรยากกว่ากัน

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

Most notions of differential geometry are formulated with the help of
Multivariable Calculus and Linear Algebra.

https://math.rutgers.edu/academics/undergraduate/

Topology is a subject where understanding basically rests on the number of examples
you have handy, and also a very widely encompassing subject.
So with more background in other subjects you will have an easier time
with obtaining a conceptual understanding.

Gyu Eun Lee
https://www.math.ucla.edu/~gyueun.lee/