Touching, as you probably consider it, does not exist. All interactions take place at a distance – like magnets. While electrons are, as particles, incredibly tiny (even compared to other things on an atomic scale), they still repel other electrons and *very forcefully so* if those other electrons get too close.
So, while an electron does not physically occupy the space in an atom, it still has claim to that space and will prevent other electrons from occupying said space.
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