DCI Darren George said: “A 49-year-old local man has been arrested on suspicion of murder and at this time we are not looking for anyone else in connection with this matter.
“We are keen that anyone with information comes forward and we are particularly keen to speak to anyone who was in the Carlton Terrace area of Swansea between 8pm yesterday and 4am this morning.
“I would like to thank the local community for their patience during significant police activity in the area.”
In a statement they said: “Officers were called at approximately 3.10am today to Carlton Terrace following reports of an incident.
DCI Darren George said: A 49-year-old local man has been arrested on suspicion of murder and at this time we are not looking for anyone else in connection with this matter.
“Significant police enquiries are on-going in the area, the deceased woman has not yet been officially identified.
“Armed officers alongside divisional units and the police helicopter continue to be in the area and a number of cordons remain in place while investigations continue.
The victim, named locally as Sammy Lee Lodwig, was found dead in a rented house at 3am following a reported stabbing in Swansea, South Wales.
“We appreciate the local community’s continued support while our investigations are ongoing.
Chanelle Jones posted a message saying: Such a young beautiful girl! RIP. Gone but not forgotten. Such a cruel world.
Teresa Ogbekhiulu, who is studying in the area, said: “It’s really alarming to have something like this happen just by me.
“It’s really sad. I didn’t hear anything, first I had seen was on my phone on the news. I had no idea what was going on and I literally just got off my bed, looked outside and saw police everywhere.”
“We hadn’t heard anything before that. It’s shocking. Stuff like this doesn’t happen in Swansea. It’s quite unusual.”
A number of cordons have been set up in the Mount Pleasant area of the city as police continue to search the area