the outer layer of the thermosphere
To reach the complete Exophere of the earth, it is usually said you will need to travel 10,00km vertically. Though its approximately 100km to leave earths oxygen rich atmosphere.
Well, its not the "outer" space, but its called the space, as it is the last layer of the atmosphere. It called "space" because its distance above the earths surface is 500km to god knows what !