range, region, limits, stage, level
域 centers on a bounded area or scope: a physical region, a range of values, or a stage within a process. The idea of limits or a defined level extends naturally from that spatial core.
域 combines 土 (earth, ground) with 或, which likely contributes the sound and the idea of a bounded area. The character originally referred to a territory or region.
The left side 土 is earth or ground, and the right side 或 looks like a fenced-off area with a weapon 戈 guarding the boundary. Picture a marked-off region of land: that is your range or stage.
For イキ, imagine stepping into a new region and taking a deep breath: 息 (いき, breath) -> イキ, as you enter the bounded area.
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area; region; district; locality
territory; domain
region; limits; stage; level
area; zone; district; quarter; section; limits; boundary
area of sea; waters
the whole area; the entire region; all parts (of)
wide area
sacred precincts; sanctuary; consecrated ground; holy ground
band; zone; range
drainage basin; catchment basin; river basin; watershed; valley
waters; water area
range (of a voice or instrument); register; compass
airspace
inside the area
regional revitalization; local revitalization
municipal area
Shinto shrine precincts
outside the area
range of one's work; one's area of responsibility; range of one's duties
broadband; wideband