MTL122

One point compactification

Extended real and complex system which is compact

Complex Analysis

Differentiability

Analogous to R and almost the same idea

implies R^2 Differentiability

Necessary condition for differentiability and the CR Equation

Partial derivatives same as in R^2

Sufficient condition for differentiability Continuity of PD and CR Equation

Connectedness

Open and Connected

Path Connectedness

Path Connected+Extra

Extra Special kind of paths line segments parallel to x and y axis

Domains in Complex

Limit of functions

Same as in R2

Functions from C to C

Can write identify the real and imaginary parts as separate fucntions

Any linear transformation is Differentiable

Important idea relating to different paths and many possibilities

Can be used to define continuity

Sequential defination essential idea that the point is not part of the sequence