Toronto police have identified the woman found tied up and stabbed to death in her apartment Tuesday evening.

Yuan (Tracy) Tian, 31, was found on her bedroom floor by her boyfriend around 6:30 p.m.

Police questioned the boyfriend at great length on Wednesday and investigators are verifying his alibi.

The lead homicide detective on the case said Friday that investigators are working on a number of theories and still don't have any suspects in the gruesome slaying.

Investigators are "keeping an open mind" about what might have happened to Tian in her apartment at 75 Talara Drive, in the Bayview Avenue and Sheppard Avenue East area, Det. Sgt. Frank Skubic said Friday.

An autopsy confirmed the cause of death to be multiple sharp force injuries to the body. The post-mortem did not indicate that the victim was sexually assaulted, Skubic said.

There were no signs of robbery at the scene. However, officers were expecting to obtain a warrant to search the apartment for evidence sometime this weekend.

Skubic did say Tian had many people visit her apartment in recent days after she placed an advertisement for a room for rent in her two-bedroom apartment.

Her brother had lived with her until he moved out earlier this summer to pursue a job in the United States, Skubic said.

Police are also pursuing leads after neighbours reported seeing a prowler in the area dressed all in black and peering into ground-floor apartment windows.

Skubic appealed to anyone with information about a peeping tom, "no matter how trivial it may seem," to contact police.

He also asked that more of Tian's friends and any former boyfriends come forward to tell police what they know of her life.

Skubic said the victim came to Canada in 2005 to further her education.

She attended both the University of Guelph and the University of Windsor and had recently obtained an economics degree.

She was looking for a full-time job before she died.

Skubic said that 33 Division will increase patrols in the neighbourhood. As well, the division will set up a command post vehicle in front of the building at 6 p.m. Friday to answer questions and take statements from neighbours and potential witnesses.

The vehicle will remain on site throughout the weekend.

The slaying is the city's 46th homicide of 2008.