A 28-year-old man was attacked at a flat in Dundasvale Court, in the Cowcaddens area of Glasgow.
He was discovered with serious injuries at around 10.10pm on Monday.
As reported in last night's Evening Times, the victim's identity was unknown, but detectives have now established he lives locally.
Police are following a positive line of enquiry.
The victim was taken to to Glasgow Royal Infirmary, where he is still receiving treatment.
Hospital staff described his condition as "serious but stable".
Police said the attack was an "isolated incident" and have increased patrols to reassure local residents.
Detective Chief Inspector Stevie Grant, of Strathclyde Police, said: "We would like to reassure members of the public, particularly the residents of Dundasvale Court flats, that we believe this assault to be an isolated incident.
"There should be no cause for concern from the local community.
"Extra patrols will be in the neighbourhood in the coming days and anyone with concerns should speak to the officers."
Anyone with any information about the incident is asked to contact police on 0141 532 3059.