The death of Mary Ward was discovered at her residence on Melrose Street in the city on Tuesday of last week, according to the Police Service of Northern Ireland (PSNI).
Police are looking to speak with anyone who was in contact with Ms. Ward on or around Wednesday, September 25, as that is when they believe she was last seen alive, six days earlier.
Ms. Ward is "the fourth woman to be murdered in Northern Ireland in just six weeks," said to Chief Superintendent Lindsay Fisher.
"This is just horrifying," the senior officer continued.
"Four families have been shattered forever by meaningless violence."