Typescript recursive string literals

Question

I want to get the union of all they keys of my object recursively that is separated by period.

For example:

type User = {
    name: string;
    age: number;
    work: {
        company: string;
        position: string;
    }
}

I want to get 'name' | 'age' | 'work' | 'work.company' | 'work.position';

This is my initial code:

type RecursiveKeys<T> = T extends number | string | boolean ? T : {[K in keyof T]: `${K}.${RecursiveKeys<T[K]>}`}[keyof T]

I suspect my mistake is in this part of my code T extends number | string | boolean. I'm not sure what condition shall I put to end my recursive