There could be instances where you would like to close specific tickets without notifying the requester that the ticket was closed. 

In such cases, you could click on the ticket from the tickets list, which would take you to the ticket details page. Within the ticket details page, to the top, you would find the "Close" option. You could click on the "Shift" key and simultaneously click on the Close option. 

This would close that particular ticket, without sending out the default notification for when "Agent Closes a Ticket", to the requester.