The Pauli exclusion principle states that only one electron can be in each quantum state. If you try to pack a large number of electrons in a small volume, the available quantum states run out. It becomes harder and harder to decrease the volume, so it is as if there was a very high pressure. This is known as the degeneracy pressure. This happens to the electrons when a star collapses, and if the star is not too massive the degeneracy pressure is able to stop the collapse.
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eigenvector commented on :
Thanks Arttu! I’ll put this in my Physics A-level paper on Tuesday if a star question comes up!