Amy Stringfellow, aged in her 20s, was found seriously injured at a house in Dryden Road, Balby, on Friday, June 5.
Emergency services were called at around 11.35pm but Amy could not be saved and was pronounced dead at the scene a short time later.
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A 45-year-old man arrested on suspicion of murder remained in police custody last night.
Tributes to Amy, named locally and on Facebook, have been paid online after details of her murder were released by South Yorkshire Police yesterday.
She was a mum, with a young daughter, and worked as a personal trainer at a gym.
One family tribute, posted on Facebook, said: “Words can’t describe how heartbroken we are’.
Amy’s aunt, Denise Elliott said: “My beautiful baby niece.
“So cruelly taken from us. I don’t know how our family can ever be the same again without you in it.
“We are totally numb. We love you more than life itself.”
Lisa Lea posted: “So sorry to hear this devastating news. Such a beautiful girl with everything to live for.”
And Shannan McNeal posted: “Totally shocked and devastated.
“What an amazing mum, daughter, sister, friend, everything.”
Sam Imray said:”Absolutely devastated, words cannot describe how sorry I am for your loss.
“Amy was a beautiful, amazing person with such a big heart.
“I loved her to bits, she was like a little sister to me.”
Greg Fishburn said Amy was a personal trainer at Hercos Gym.
He posted “I feel physically sick hearing this tragic news.
“She was such a great girl, a PT at Hercos Gym who always had a smile on her face and filled the gym with laughter.”
Alex Grave described Amy as a ‘lovely girl’ and former school friend Sophie McGowan said: “I just can’t even believe this has happened. It is such a waste of a young life.”
Anyone with information to help detectives investigating the murder should call South Yorkshire Police on 101 and quote incident number 904 of June 5.