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"I am not a speed reader. I am a speed understander."
- Isaac Asimov

Rotating Hollow Planetoid Habitat  
  An asteroid (or planetoid) hollowed out, spun for artificial gravity, used as a habitat.  

This is an early expression of this idea; using the solid metal core of an ancient planet actually works better than an asteroid.

It was nearly twenty-four hours later that they finally approached their destination, a tiny, five-mile world of solid metal, a part of the nickel-steel core of some long vanished planet. Its surface turned swiftly beneath them, flashing around in moments as they watched, a surface made up of great crags and clefts of metal, broken, barren masses of metal.
“Lord — it would be impossible to establish a city on the surface of that top!” exclaimed one of the Patrolmen. “The centrifugal spin there would throw anything off into space.”
“How about the inside of it then?” asked one of the guards, smiling at him...
"...When the colony was established, the whole interior was carved out with atomic burners — burned the stuff out into gas, and let it escape. The shell’s about half a mile thick. Inside, the centrifugal force gives an acceleration just equal to one earth gravity, we’re up to speed, and you can see we have about an earth-weight away from it now. And an artificial sun gives plenty of light.”
Technovelgy from Electronic Siege, by John W. Campbell.
Published by Wonder Stories in 1932
Additional resources -

Many asteroids are just piles of rubble, held together by what little gravity comes from the mass of the objects. It wouldn't be possible to spin them for artificial gravity, or to excavate them.

This idea resurfaced in the 1960's:

In 1963, Dandridge Cole wrote Exploring the Secrets of Space: Astronautics for the Layman with I. M. Levitt. In this book they suggested hollowing out an ellipsoidal asteroid about 30 km long, and rotating it about its major axis to simulate gravity. By reflecting sunlight inside with mirrors, and creating, on its inner surface, a pastoral setting an asteroid could be transformed into a permanent space colony. Cole and Cox also envisioned that asteroids would provide the raw materials to form the basis of a spacefaring civilization. And, that asteroidal materials would also serve terrestrial needs. In their view these materials could be transported using mass drivers or linear motors. Cole’s work largely presages that of Gerard K. O’Neill by more than a decade.

For a very early use of the phrase, see hollow asteroid (1944) from Juke Box Asteroid by Joseph Farrell.

Hollowed-out asteroid habitats are also called "Cole bubbles" after Dandridge Cole. (See also the section asteroid habitats in Project Rho. Thanks also to @fredkiesche for tips.)

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Additional resources:
  More Ideas and Technology from Electronic Siege
  More Ideas and Technology by John W. Campbell
  Tech news articles related to Electronic Siege
  Tech news articles related to works by John W. Campbell

Rotating Hollow Planetoid Habitat-related news articles:
  - Is A Hollow Rotating Asteroid Habitat Practical?
  - Restructure An Asteroid, Spin It, Get A 'Space Habitat' With Gravity?

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