I have been searching for a proper explanation to " The Injective Mapping Theorem " in R. G. Bartle which deals with derivatives of vector functions, but most of the results I found till now gives only definition and properties of Injective mapping of functions
The Inversion Mapping theorem as in R. G. Bartle
1.) Is the name of the concept ( or theorem ) different or is Bartle the only one who deals with it ?
2.) Can anyone give a good explanation of it I need it in terms of Real Analysis ,cause I haven't done much of topology or other analysis subjects, can you please refer to some sources.
3.) What I understood of it was that if the differential is continuous and injective then the function is also injective in the neighbourhood of the point of differentiation.
( If my understanding is right ) can I also know why it is not injective over the entire domain of f and only in the neighbourhood of the point of differentiation, it would be clear if there is a counter example.