open the door
To allow more action or discussion; give a chance.
Learning to read and write opens the door to a better job and better living conditions.
Raising the tax rates will open the door to more help for older people.
open-door policy
A policy that states that newcomers are welcome to join the company, firm, or country in question.
During the nineteenth century the United States had an open-door policy regarding immigration.
show the door
To ask (someone) to go away.
Ruth was upsetting the other children, so I showed her the door.
Our neighbors invited themselves to the party and stayed until Harry showed them the door.