Write code segment that closes a desktop application once button “EXIT” is clicked.

Sure, here is a simple example of how you might do this in Python using the Tkinter library for GUI:

import tkinter as tk

def close_app():
    root.destroy()

root = tk.Tk()
exit_button = tk.Button(root, text='EXIT', command=close_app)
exit_button.pack()

root.mainloop()

In this code:

1. We first import the tkinter module.
2. We define a function close_app that will close the application. This function calls the destroy method on the root window, which closes the application.
3. We create a root window using tk.Tk().
4. We create a button labeled 'EXIT'. The command parameter is set to our close_app function, meaning this function will be called when the button is clicked.
5. We use the pack method to add the button to the window.
6. Finally, we start the application's main loop with root.mainloop(). This loop will run until the application is closed, either by clicking the 'EXIT' button or using a standard window close control.