personal space 
noun [mass noun]
The physical space immediately surrounding someone, into which encroachment can feel threatening or uncomfortable: he was invading her personal space...
- The fact that Annie doesn't have a zoom lens meant that she had to invade that person's personal space to get the detail she required.
- The concepts of personal space and physical comfort were quite foreign to the typical Jamaican commuter back in those days.
- He invades personal space, standing mere inches away from his staff while playing the innuendo card with a heavy-handedness that makes his point painfully obvious.