I heard a conjecture "3-dim positively curved Alexandrov space is of the form S^3/J.(I cannot make sure my statement is accurate). What is the classification of n-dim positively curved Alexandrov space? And if a n-dim positively curved Alexandrov space has a totally (quasi)geodesic subset,then the classification? Maybe it's stupid to ask such a big quesiton,I just want to know what we have known about this.can someone recommend some books or papers on it?