TypeScript definitions for Server-Sent Events
According to your definition file, I'm assuming there's a global class called EventSource

If that's the case, I have the following improvements:


Avoid Function (or Object or Array), describe the signature accurately (like you did with onmessage). If you don't know the return type or the argument, apply any liberally. At least you're explicit about not knowing.
TypeScript has literal string, number and enum types, so you could do something like CONNECTING: ReadyState.CONNECTING 


All in all, it's a fine definition file.