It's hard to answer a hypothetical. Is there a fact situation involved here that you could describe for me?
Where do you live?
Have there been any criminal charges for assault laid?
Does this involve spouses?
If this were a criminal matter, then he would have assaulted you because he perpetrated unwanted contact upon you.
There is no "personal space" criminal law, but if someone is getting in your face and you feel threatened, then that's a different charge.
The racial slurs are irrelevant, I'm afraid. It will gain you sympathy from investigators, and give you a possible defense of provocation should a civil suit be launched, but I really can't see that happening here anyway. Clearly the other fella suffered no damages.
If he wants to sue for discrimination or abuse of authority, then it would be against your employer moreso than you personally, since as far as you knew you were carrying out your employers policies and may well have been doing so in fact.
Now, the transit police are different from normal police, and since you probably belong to a union I'll refrain from commenting further on your personal liability while carrying out your employment duties. Your union has the sole right and obligation to represent you in those matters, so it doesn't really matter what I think while sitting here at my kitchen table.
So, to answer your question, there's no defined "personal space" in law the breach of which creates liability. But instigating an unwanted touching is an assault by strict definition. Having said that, the fact that you were at work at the time complicates things severely. Be co-operative with your employer, and if you have any serious concerns, consult your union steward if you have one.
I hope this answers your question, Trab.
please accept this answer so that I may receive credit for the time and attention I've put into your matter.