The DUP leader was speaking at the first Killarney Economic Conference
The leader of Northern Ireland's Democratic Unionist Party (DUP) says Brexit is not about "pulling up the drawbridge" between the Republic and the North.
Arlene Foster was speaking at the Killarney Economic Conference in Co Kerry on Saturday.
Mrs Foster said: "I often think that Northern Ireland and the Republic of Ireland are like a semi-detached house.
"The houses may look the same on the outside, but, inside, they look different and we do many things very differently.
"But no matter how contrasting the interiors are, they are tied together and part of the same neighbourhood and what happens on one side of the fence inevitably has an impact on the other.
"I know that we are rivals in some respects, but in so many ways success for one of us is success for the other.
"As we chart a new course for the future, it is not in our interests to see the Republic of Ireland do anything other than prosper.
"Nor does it help any of us if we let the challenges that Brexit brings deflect us from the opportunities that will exist in the future.
"We will continue to have our own identities and for our part we will no longer be members of the European Union, but our futures will still be closely connected."
On Brexit, Mrs Foster added: "The Democratic Unionist Party supported the UK leaving the European Union but in so doing Brexit is not about pulling up the drawbridge, building a wall and cutting ourselves off from our nearest neighbours.
"But we must all recognise that change is coming as a result of the referendum.
"It is our job as politicians to help shape that change but to do so in a way that ensures that those economic, cultural and social ties that have endured through difficult times and have thrived through better ones continue into the future.
"We want to avoid a cliff edge for businesses by having a strictly time limited implementation period."
Speaking about the EU and Northern Ireland, Mrs Foster said: "We value the contribution that EU migrants have made and continue to make to our economy and society and we will support a new border policy that is strong but sensible.
"We may well be leaving the European Union but we are not leaving Europe and we want businesses, students and researchers to continue to have opportunities to foster links with their neighbours through continued participation in future EU programmes that are cost-effective and bring tangible benefits."