Electron Degeneracy

1. As the core is compressed, heat is generated. 
2. The added heat excites the electrons, freeing them to form an electron cloud. 
3. As this cloud grows, it generates its own pressure to counteract the gravitational forces  independent fusion and temperature.
4. Stars whose mass is not large enough for gravity to overcome this "electron degenerate" pressure (about 1.4 Solar Masses) will stop compressing. 
5. Since these stars no longer compress, the fusion process will slow down and the star will begin to cool. This is known as a "White Dwarf". 
Red Giants