Tributes have been paid to the woman and her two children who were killed in a shooting in Co Fermanagh.
They have been named as Vanessa Whyte, 45, and her children, 14-year-old James Rutledge and Sara Rutledge, who was 13.
They were shot at their home in Maguiresbridge yesterday.
A man remains in a serious condition in hospital.
One line of inquiry being investigated by police is that what happened was a triple murder and attempted suicide.
Ms Whyte worked as a veterinary surgeon for the Department of Agriculture, Environment and Rural Affairs (DAERA) in Northern Ireland.
PSNI Detective Chief Inspector Neil McGuinness said: "Today, our thoughts remain with those loved ones whose worlds have been torn apart.
"Our investigation is continuing and I am keen to reiterate our appeal for anyone with information to get in touch.
"I am particularly keen to hear from anyone who had spoken to Vanessa, Sara or James over the last few weeks. If you are someone that Vanessa, Sara or James may have confided in, please come and speak to us.
"Any information, no matter how small or insignificant it may seem could prove crucial to our investigation," he said.
The PSNI said that it is aware of "ongoing speculation and the sharing of imagery on social media" in relation to the shooting.
"We would ask that people refrain from sharing misinformation or images as this may ultimately have a negative impact on the criminal justice process," it added.
Vanessa Whyte 'a valued member' of staff - department
DAERA said that it is "deeply saddened" by the death of Ms Whyte and her children "in these tragic circumstances".
"Vanessa was a valued member of our Veterinary Services and Animal Health Group and a hugely respected member of the veterinary profession," the department's permanent secretary Katrina Godfrey said in a statement.
"She will be greatly missed by all who worked alongside her.
"On behalf of the department, we offer our sincere condolences to her family, friends and all those in the community impacted by her and her children's deaths.
"They will remain in our thoughts and prayers in the difficult days and months ahead as they and we come to terms with the loss."
Chief Veterinary Officer Brian Dooher said that Ms White was a highly respected member of the DAERA Veterinary Services and Animal Health Group, a devoted mother and active member of her community.
"Many of us had the privilege of knowing Vanessa personally and she was hugely admired by all those who came across her," he said.
"The loss we feel today is immense and it has profoundly affected us.
"The next few days, weeks and months will be difficult for all who knew her - especially her family.
"We are thinking of her family, friends and neighbours at this time and we ask that people give everyone the time and space to come to terms with their loss at this difficult time."
Church of Ireland Rector of Maguiresbridge, Reverend Lindsey Farrell, said: "The community are devastated they're in a state of shock
"None of us expected what has come to pass, but this is a strong community and as a church and as a wider community, we are uniting behind this family."
Catholic Bishop of Clogher Larry Duffy said he was "deeply shocked and saddened by the tragic news of the death of a mother and two children near Maguiresbridge yesterday".
"While we do not know all the circumstances surrounding this tragedy, I am very aware that the news is causing deep distress in the community of Co Fermanagh and beyond," he said.
"I assure the family of the deceased, and everyone affected by this tragedy, of my prayers and assure them of the prayerful support of the wider community."
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Yesterday, Superintendent Robert McGowan confirmed that all four people were from the same household and suffered gunshot wounds.
Ms Whyte and one of the children were pronounced dead at the scene on Drummeer Road.
The second child died later in hospital.
Police said they received a 999 call from someone inside the house appealing for help shortly before 8am yesterday.
Officers were despatched immediately from Enniskillen station around 13km away.
When they arrived at the property, they found four people inside with gunshot wounds.
James and Sara were both pupils at Enniskillen Royal Grammar School.
In a statement, the school said: "It is with a very heavy heart and much sadness that we mourn the loss of two vibrant and much valued pupils".
It continued: "As a school community we are very much thinking of the family and send our heartfelt condolences to them at this difficult time".
The school said its senior leadership team and pastoral staff are working with the Education Authority critical incident team to support pupils and staff.
Helplines
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Additional reporting PA
