Police believe a series burglaries or attempted burglaries that took place last week are linked.
The incidents occurred on the same day in the Lansdowne Road and Manor Road areas of Worthing, police said.
Officers were called to a flat in Lansdowne Road at 5.34am on Tuesday, October 9.
An elderly occupant disturbed a man who had gained entry through French doors, police said.
She shouted at the man, who turned and fled, according to police.
Police describe him as white, aged 16-18, 5ft 5ins to 5ft 6ins, of medium build, clean shaven with neat and tidy short dark brown hair and wearing a dark grey waterproof jacket, black jeans and black trainers.
Shortly before 7am the same day, the occupant of a flat in Manor Road saw someone put their hand through a ground floor window.
The suspect ran off when shouted at, said police.
Around 7.30am, a handbag and mobile phone were stolen from the kitchen of a house in Manor Road, confirmed police.
The victim alerted police officers who were in the area making house-to-house enquiries about the earlier incidents.
At 9.30am, a break-in was discovered at a ground floor flat in Lansdowne Road where the occupant was away.
A neighbour reported challenging a man who was seen climbing a neighbour’s garden fence around 5.25am, said police.
He claimed that he had lost his cat and ran off.
Detective Constable Jon Berisford said: “We’d like to hear from anyone with any information about these incidents or those involved.
“Please report online or call 101 quoting serial 187 of 09/10.
“I would also urge people to ensure that their homes are secure, especially overnight and early mornings.”