Basics of Topology

 

 

In a Nut Shell:  Curves and domains in two and three dimensions can be classified in

different ways that are important when applying Green's Theorem and Stokes Theorem.

The table below provides definitions of terms related to the topology of curves and domains.

 

 

 

Definitions:  Let  D  be the domain

 

     

 

Simple Curve

 

 

 

The curve does not intersect itself

 

Closed Curve

 

 

 

The terminal point coincides with the initial point of the curve

 

Open Domain

 

 

 

The domain contains points inside but not on the boundary

of the domain

 

Closed Domain

 

The domain contains points within and on the boundary

of the domain

 

 

Connected Domain

 

 

 

Any two points in the domain can be joined by a path within

the domain

 

Simply Connected

Domain

 

 

Every simple closed curve in the domain encloses only points

within the domain

 

                        

Click here to return to discussion of Green's Theorem.

 

 

 



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