ceoln, 
Oh hey maybe this would be a fun place to talk about my half-baked amateur #math and possibly #topology ideas!
Say I have a semi-metric space where for every point P and real distance D > 0, there is at least one point Q where distance(P,Q)=D.
Is that space interesting in any way? Does it have a name or set of named properties?
Earlier weblog entry (using a rule about accumulation points rather than the PQD thing): https://ceoln.wordpress.com/2024/02/09/semi-metric-woolgathering/