No funeral arrangements have yet been made for 31-year-old murder victim Laura Marshall, following the discovery of her body on Sunday.
It is understood that the family have not yet recieved her remains.
A man was still being quizzed by police on Tuesday night over the murder of the woman, who has been described as “popular” and “outgoing”.
The PSNI said on Tuesday afternoon that officers had applied for and been granted an extra 36 hours to question the 36-year-old man being held over the killing.
Ms Marshall’s body was found at her apartment in the former Johnston Allen building on Victoria Street, and, following a post-mortem, the PSNI launched a murder probe the next day.
The woman’s uncle had also been the victim of murder.
A prominent republican, Sam Marshall was shot dead by loyalists outside the town’s police station in 1990.
Joe Nelson, SDLP councillor in the town, said he knew the Marshall family to be “decent people” with “republican inclinations” – adding that he was not aware of any suggestion of any political element to the latest incident.
He said that he had a daughter around the same age as the victim, adding: “There is still shock [in the town]. The girl in question seemed to be very, very popular, and seemed to have a big number of friends on Facebook.”
It was on social media that many chose to air their messages of sympathy.
Dean Oxby described her as a “very popular and outgoing inspirational woman who can always put a smile on your face”.
He added: “You made many friends around the world where you have travelled on your journeys and they are sadly touched by the news of your death.”
A young woman called Amy Marshall wrote on Facebook in the wake of the killing: “I just wish I could speak to you one last time.
“You were the kindest person...but at least you are happy now in Heaven with Granny Alice looking down on us all.”
Ulster Unionist councillor Kyle Savage branded her death “incredibly sad”.
The PSNI have asked for anyone who had contact with Ms Marshall over the weekend to contact detectives at Mahon Road on 101 or call Crimestoppers on 0800 555 111.